Deck 7: Linear Regression

Question 1

The graph of the simple linear regression equation is a(n)

A)ellipse.
B)hyperbola.
C)parabola.
D)straight line.

Answer 1

straight line.

Question 2

In a simple linear regression model, y = ß₀ + ß₁x + ε B₁ represents the

A)intercept.
B)slope of the true regression line.
C)mean value of x.
D)error term.

Answer 2

slope of the true regression line.

Question 3

A ___________ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationship between the variables.

A)contingency table
B)scatter chart
C)Gantt chart
D)pie chart

Answer 3

scatter chart

Question 4

What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?

A)31.89
B)19.32
C)18.43
D)15.32

Question 5

When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is

A)positive.
B)zero.
C)negative.
D)infinite.

Question 6

The _______________ is the range of values of the independent variables in the data used to estimate the regression model.

A)confidence interval
B)codomain
C)experimental region
D)validation set

Question 7

Prediction of the mean value of the dependent variable y for values of the independent variables x₁, x₂, . . . , x_q that are outside the experimental range is called

A)dummy variable.
B)overfitting.
C)extrapolation.
D)interacton.

Question 8

The least squares regression line minimizes the sum of the

A)differences between actual and predicted y values.
B)absolute deviations between actual and predicted y values.
C)absolute deviations between actual and predicted x values.
D)squared differences between actual and predicted y values

Question 9

In the graph of the simple linear regression equation, the parameter $B _ { 0 }$ represents the ___________ of the regression line.

A)slope
B)x-intercept
C)y-intercept
D)end-point

Question 10

In the simple linear regression model, the ____________ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.

A)constant term
B)error term
C)model parameter
D)residual

Question 11

The ____________________ is a measure of the error that results from using the estimated regression equation to preduct the values of the dependent variable in the sample

A)sum of squares due to regression (SSR)
B)error term
C)sum of squares due to error (SSE)
D)residual

Question 12

Prediction of the value of the dependent variable outside the experimental region is called

A)interpolation.
B)forecasting.
C)averaging.
D)extrapolation.

Question 13

In a simple linear regression analysis the quantity that gives the amount by which the dependent variable changes for a unit change in the independent variable is called the

A)coefficient of determination.
B)slope of the regression line.
C)correlation coefficient.
D)standard error.

Question 14

In a linear regression model, the variable (or variables) used for predicting or explaining values of the response variable are known as the ________________. It(they) is(are) denoted by x.

A)dependent variable
B)independent variable
C)residual variable
D)regression variable

Question 15

_____ is a statistical procedure used to develop an equation showing how two variables are related.

A)Regression analysis
B)Data mining
C)Time series analysis
D)Factor analysis

Question 16

A procedure for using sample data to find the estimated regression equation is

A)point estimation.
B)interval estimation.
C)the least squares method.
D)extrapolation.

Question 17

The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the

A)constant term.
B)error term.
C)residual.
D)model parameter.

Question 18

A regression analysis involving one independent variable and one dependent variable is referred to as a

A)factor analysis.
B)time series analysis.
C)simple linear regression.
D)data mining.

Question 19

In a linear regression model, the variable that is being predicted or explained is known as _____________. It is denoted by y and is often referred to as the response variable.

A)dependent variable
B)independent variable
C)residual variable
D)regression variable

Question 20

In the graph of the simple linear regression equation, the parameter $B _ { 1 }$ is the ___________ of the regression line.

A)slope
B)x-intercept
C)y-intercept
D)end-point

Question 21

Regression analysis involving one dependent variable and more than one independent variable is known as

A)simple regression.
B)linear regression.
C)multiple regression.
D)none of these.

Question 22

The ___________ is a measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.

A)residual
B)coefficient of determination
C)dummy variable
D)interaction variable

Question 23

______________ refers to the degree of correlation among independent variables in a regression model.

A)Multicollinearity
B)Tolerance
C)Rank
D)Confidence level

Question 24

A variable used to model the effect of categorical independent variables in a regression model is known as a

A)dependent variable.
B)response.
C)dummy variable.
D)predictor variable.

Question 25

__________________ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.

A)Interval estimation
B)Hypothesis testing
C)Statistical inference
D)Point estimation

Question 26

What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?

A)2.32
B)0.43
C)0.19
D)0.89

Question 27

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below? ​

A)The residuals have a increasing variance as the dependent variable increases.
B)The model captures the relationship between the variables accurately.
C)The regression model follows the standard normal probability distribution.
D)The residual distribution is consistently scattered about zero.

Question 28

The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart?​

A)model is time-invariant.
B)model captures the relationship between the variables accurately.
C)residuals are not independent.
D)residuals are normally distributed.

Question 29

The process of making conjecture about the value of a population parameter, collecting sample data that can be used to assess this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as

A)postulation.
B)hypothesis testing.
C)statistical inference.
D)empirical research.

Question 30

The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as

A)inductive inference.
B)deductive inference.
C)statistical inference.
D)Bayesian inference.

Question 31

________________ is used to test the hypothesis that the values of the regression parameters B₀, B₁, B2, ... B_q are all zero.

A)An F test
B)A t test
C)The least squares method
D)Extrapolation

Question 32

Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?

A)a multiple regression model
B)quadratic regression model
C)a simple regression model
D)a least squares regression model

Question 33

A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called

A)a residual.
B)the coefficient of determination.
C)a dummy variable.
D)interaction.

Question 34

The coefficient of determination

A)takes values between -1 to +1.
B)is equal to zero for a perfect fit.
C)is equal to negative one for the poorest fit.
D)is used to evaluate the goodness of fit.

Question 35

The _____________ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.

A)residual
B)tolerance factor
C)confidence level
D)accuracy level

Question 36

The prespecified value of the independent variable at which its relationship with the dependent variable changes in a piecewise linear regression model is referred to as the

A)milestone.
B)knot.
C)tipping point.
D)watchpoint.

Question 37

The degree of correlation among independent variables in a regression model is called

A)multicollinearity.
B)interaction.
C)the coefficient of determination.
D)the sum of squared errors (SSE).

Question 38

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​

A)The residuals have a constant variance.
B)The model fails to capture the relationship between the variables accurately.
C)The model over predicts the value of the dependent variable for small values and large values of the independent variable.
D)The residuals are normally distributed.

Question 39

A normally distributed error term with mean of zero would

A)have values that are symmetric about the variance.
B)allow more accurate modeling.
C)yield biased regression estimates.
D)be a hyperbolic curve.

Question 40

The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? ​

A)The residuals have a constant variance.
B)The model captures the relationship between the variables accurately.
C)The model underpredicts the value of the dependent variable for intermediate values of the independent variable.
D)The residual distribution is not normally distributed.

Question 41

Listed below is a company's sales in the period 2000 to 2011 along with the national income of the country, where the
business is set up. Test whether each of the regression parameters β₀ and β₁ is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters?

Question 42

Listed below is data on profit and market capitalization for a sample of 15 different firms in U.S.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between market capitalization and profit?
b. Use the data to develop an estimated regression equation that could be used to estimate a firm's profit based on its market capitalization. What is the estimated regression model?
c. What is the predicted profit for the market capitalization of 70,721.3 (million)?

Question 43

Listed below is a company's sales in the period 2000 to 2011 along with the national income of the country, where the
business is set up.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between the
National Income and the Company's sales in the period 2000 to 2011?
b. Use the data to develop an estimated regression equation that could be used to estimate the company's sales
based on the national income. What is the estimated regression model?

Question 44

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below.
a. Determine the estimated multiple linear regression equation that can be used to predict
the annual income given number of years school completed (Education), length of tenure
in current employment, and age.
b. Use the F test to determine the overall significance of the regression relationship.What is the conclusion at the 0.05 level of significance?

Question 45

__________ is the data set used to build the candidate models.

A)Range
B)Codomain
C)Validation set
D)Training set

Question 46

_____________ refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.

A)Interaction
B)Multicollinearity
C)Autocorrelation
D)Covariance

Question 47

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
a. Develop an estimated linear regression equation with the factor x₁ as the independent variable.Test for a significant relationship between factor x₁ and yield at the 0.05 level of significance.
b. How much of the variation in the sample values of yield does the model in part (a) explain?

Question 48

A research team in at the Gonzaga University is interested in predicting a student's overall university GPA if his/her high school GPA is known. Assume that a random sample of 20 students is selected from the data listed below.
a. Develop a scatter chart for these data with High School GPA as the independent variable.What does the scatter chart indicate about the relationship between high school GPAs and overall university GPA?
b. Develop an estimated regression equation showing how high school GPA is related to overall university GPA.What is the estimated regression model?
c. What is the predicted overall university GPA of Sophia, a student who has been admitted to Gonzaga
University, with 3.40 high school GPA?

Question 49

Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population is termed as

A)approximation.
B)hypothesizing.
C)overfitting.
D)postulating.

Question 50

A research center is interested in investigating about height and age of children who are between 5 to 9 years old.
In order to do this, a sample of 15 children is selected and the data is given below.
a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?
b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?
c. How much of the variation in the sample values of height does the model estimated in part (b) explain?

Question 51

A researcher wanted to study effect of two factors, x₁ and x₂, on yield (y). The observations are given below.
a. Develop an estimated regression equation with both factors x₁ and x₂ as the independent variables. Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β₀, β₁, and β₂ is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters?
b. How much of the variation in the sample values of y does the model in part (a) explain?

Question 52

A survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 employees is selected and the data is given below.
a. Check if the F test leads to conclude that an overall regression relationship exists. If yes, use the t test to
determine the significance of each independent variable. What is the conclusion for each test at the 0.05 level of significance?
b. Remove all independent variables that are not significant at the 0.05 level of significance from the estimated
regression equation. What is your estimated regression equation in this case?

Question 53

Assessing the regression model on data other than the sample data that was used to generate the model is known as

A)approximation.
B)cross-validation.
C)graphical validation.
D)postulation.

Question 54

A student is interested in studying the impact of number of books referred by students on a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data is given below.
a. Develop an estimated regression equation using number of books referred and the number of lectures attended to predict the final grade on the course.
b. Joseph referred 4 books and attended 19 lectures. What is his predicted final score on the course?

Question 55

A student is interested in studying the impact of number of books referred by students on a statistics course and the number of lectures they attended on the final grade on the course. A sample of 25 students is selected and the data is given below.
a. Use the F test to determine the overall significance of the relationship. What is your conclusion
at the 0.05 level of significance? Use the t test to determine the significance of each independent
variable? What are your conclusions at the 0.05 level of significance?
b. How much of the variation in the final grade does the model in part (a) explain?

Question 56

_____________ refers to the data set used to compare model forecasts and ultimately pick a model for predicting values of the dependent variable.

A)Codomain
B)Training set
C)Validation set
D)Range

Question 57

The data listed below is the average personal income and personal consumption expenditures based on the survey
conducted in the year 1995 to 2009 in U.S.
a. Develop a scatter chart for the above data. What does this chart indicate about the relationship between average
personal income and personal consumption expenditure?
b. Develop an estimated regression equation showing how personal consumption expenditure is related personal
income.
c. What proportion of variation in the sample values of proportion of personal consumption expenditure does this
model explain?

Question 58

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10
cars is selected and the data is shown below.
a. Develop a scatter chart for these data with age of cars as the independent variable. What does the scatter chart
indicate about the relationship between age of a car and the annual maintenance cost?
b. Use the data to develop an estimated regression equation that could be used to predict the annual maintenance
cost given the age of the car. What is the estimated regression model?

Question 59

The data listed below is the average personal income and personal consumption expenditures based on the survey
conducted in the year 1995 to 2009 in U.S.
a. What is the 95 percent confidence interval for the regression parameter β₁? Based on this interval, what
conclusion can you make about the hypotheses that the regression parameter β₁ is equal to zero?
d. What is the 95 percent confidence interval for the regression parameter β₀? Based on this interval, what
conclusion can you make about the hypotheses that the regression parameter β₀ is equal to zero?

Question 60

A survey is conducted to determine whether the age of car influences the annual maintenance cost. A sample of 10 cars is selected and the data is shown below.
a. Test whether each of the regression parameters β₀ and β₁ is equal to zero at a 0.05 level of significance.
b. Interpret the estimated regression parameters? Are these interpretations reasonable?

Question 61

Consider the below data which is based on a company's sales in the period 2000 to 2011 along with the national income of the country, where the business is set up.
a. Develop a scatter chart for these data, treating the national income as the independent variable. Does a simple linear regression model appear to be appropriate?
b. Develop an appropriate estimated regression equation to predict the company's sales, given the national income. How much variation in the sample values of company's sales is explained by this regression model

Question 62

The multiple regression model represents pricing for residential housing in a certain market. Predicted Price = 19,856.56 + 6985.25 bedrooms + 87.53 square foot. A house in the local market has 4 bedrooms and 2500 square feet of living area. Use the multiple regression model to determine the predicted price.

Question 63

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.
​ ​
​
​
a. Develop an estimated quadratic regression equation for the data. How much variation in the sample values of cost/unit does this regression model explain?
b. Is the overall regression relationship significant at a 0.05 level of significance? If so, then test the relationship between the independent variable and the dependent variable at a 0.05 level of significance.

Question 64

A multiple regression model has the form = 10 + 2 x₁ + 12 x₂. As x1 increases by 1 unit (holding x₂ constant), is expected to increase by how many units?

Question 65

The multiple regression model represents pricing for residential housing in a certain market. Predicted Price ̂ = 19,856.56 + 6,985.25 bedrooms + 87.53 square foot. A house in the local market has 5 bedrooms and 3,200 square feet of living area. Use the multiple regression model to determine the price and the residual if the house sells for $352,200.

Question 66

A production company is studying the relationship between the average cost/unit and number of units produced in a batch. A sample of 10 batches is selected and the data is given below.
​
a. Develop a scatter chart for these data. What does the scatter chart indicate about the relationship between average cost/unit and number of units produced?
b. Regardless of your answer to part (a), develop an estimated simple linear regression equation for the data. How much variation in the sample values of cost/unit is explained by this regression model?

Question 67

Give an estimated simple linear regression equation of = 46.2 + 589.2x with a coefficient of determination R^2 of 0.7523, interpret the coefficient of determination for this equation.
​

Question 68

The multiple regression model represents pricing for residential housing in a certain market. Predicted Price ̂ = 19,856.56 + 6,985.25 bedrooms + 87.53 square foot. A house in the local market has 4 bedrooms and 2,200 square feet of living area. Use the multiple regression model to determine the predicted price.

Question 69

The multiple regression model represents pricing for residential housing in a certain market. Predicted Price ̂ = 19,856.56 + 6,985.25 bedrooms + 87.53 square foot. A house in the local market has 5 bedrooms and 3,500 square feet of living area. Use the multiple regression model to determine the predicted price and the residual if the house sells for $360,200.

Question 70

Given the partial Excel output from a multiple regression, formulate the regression model.
​
​ ​

Question 71

A multiple regression model has for predicted heart rate is as follows: heart rate = 10 - 0.4 run speed + 12 body weight. As the run speed increases by 1 unit (holding body weight constant), heart weight is expected to increase by how much?