Deck 14: Introduction to Linear Regression and Correlation Analysis

Question 1

A study was recently conducted by a Minor League Baseball team to determine whether there is a correlation between money spent at games on concessions and the game inning. In this study, the independent variable would be the game inning.

Answer 1

True

Question 2

A cellular phone service provider believes that there is negative correlation between the minutes used by its customers and the age of the customer. To test this, the following would be the appropriate null and alternative hypotheses: H0 : ρ = 0.0 Ha : ρ ≠ 0.0

Answer 2

False

Question 3

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

Answer 3

False

Question 4

A correlation of -0.9 indicates a weak linear relationship between the variables.

Question 5

If two variables are related in a positive linear manner, the scatter plot will show points on the x,y space that are generally moving from the lower left to the upper right.

Question 6

When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

Question 7

The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

Question 8

A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances. A sample of n = 20 customers was selected and the correlation was calculated to be +0.40. If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of .05, the correct null and alternative hypotheses to test are: H0 : r = 0.0 Ha : r ≠ 0.0

Question 9

A perfect correlation between two variables will always produce a correlation coefficient of +1.0

Question 10

In developing a scatter plot, the decision maker has the option of connecting the points or not.

Question 11

In conducting a hypothesis test for a correlation, the correct probability distribution to use is the F distribution.

Question 12

When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

Question 13

A research study has stated that the income earned by working individuals is correlated at a .64 value with the years of experience of the individual. Given this, the points of the scatter plot would fall on an inclined straight line that has a slope equal to .64.

Question 14

A dependent variable is the variable that we wish to predict or explain in a regression model.

Question 15

If the correlation coefficient for two variables is computed to be a -0.70, the scatter plot will show the data to be downward sloping from left to right.

Question 16

A scatter plot is useful for identifying a linear relationship between the independent and dependent variable, but it is not particularly useful if the relationship is curvilinear.

Question 17

A bank is interested in determining whether its customers' checking balances are linearly related to their savings balances. A sample of n = 20 customers was selected and the correlation was calculated to be +0.40. If the bank is interested in testing to see whether there is a significant linear relationship between the two variables using a significance level of 0.05, the value of the test statistic is approximately t = 1.8516.

Question 18

A correlation coefficient computed from a sample of data values selected from a population is called a statistic and is subject to sampling error.

Question 19

Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

Question 20

The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

Question 21

If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.

Question 22

If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

Question 23

A university study indicated that a correlation of -0.7 was found between the number of hours spent playing video games and a student's GPA. This means that the more time spent playing video games, the lower the overall GPA.

Question 24

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: If the university wished to test the claim that the correlation between hours worked and GPA is negative, the following null and alternative hypotheses would be appropriate: H0 : ρ < 0.0 Ha : ρ ≥ 0.0

Question 25

In developing a simple linear regression model it is assumed that the distribution of error terms will be normally distributed for all levels of x.

Question 26

The fact that teachers' salaries in Wisconsin are correlated with egg prices in Texas means that the two variables are spuriously correlated since a change in one variable could not cause the change in the other.

Question 27

If two variables are uncorrelated, the sample correlation coefficient will be r = 0.00.

Question 28

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: The correlation between these two variables is approximately -.461

Question 29

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

Question 30

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: In this study the independent variable is the number of hours worked off campus per week.

Question 31

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: The test statistic for testing whether the two variables are significantly correlated is approximately z = 1.56.

Question 32

When a pair of variables has a positive correlation, the slope in the regression equation will always be positive.

Question 33

When the correlation coefficient for the two variables was -0.23, it implies that the two variables are not correlated because the correlation coefficient cannot be negative.

Question 34

Given a sample correlation r = -0.5 and a sample size of n = 30, the test statistic for testing whether the two variables are significantly correlated is approximately t = -3.055.

Question 35

You are given the following sample data for two variables: Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

Question 36

If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

Question 37

You are given the following sample data for two variables: The sample correlation coefficient for these data is approximately r = 0.755.

Question 38

In conducting a hypothesis test on the correlation between a pair of variables, we assume that each variable is normally and independently distributed.

Question 39

Given a sample of size n = 15 and a sample correlation of r = 0.7, the value of the test statistic for conducting a hypothesis test of the correlation is t = 3.53.

Question 40

In a simple regression model, the slope coefficient represents the average change in the independent variable for a one-unit change in the dependent variable.

Question 41

Assume that we have found a regression equation of = 3.6 - 2.4x, and that the coefficient of determination is 0.72, then the correlation of x and y must be about 0.849.

Question 42

Given a sample of data for use in simple linear regression, the values for the slope and the intercept are chosen to minimize the sum of squared errors.

Question 43

In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Given this, the sample correlation coefficient is known to be positive.

Question 44

The sign on the intercept coefficient in a simple regression model will always be the same as the sign on the correlation coefficient.

Question 45

Given a regression equation of = 16 + 2.3x we would expect that an increase in x of 2.0 would lead to an average increase of y of 4.6.

Question 46

You are given the following sample data for two variables: The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.

Question 47

State University recently randomly sampled seven students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: A regression model with HOURS as the independent variable has an R-square equal to approximately .46.

Question 48

If the correlation between the dependent variable and the independent variable is negative, the standard error of the regression slope coefficient in a simple linear regression model will also be negative.

Question 49

If the correlation of x and y is -0.65, then coefficient of determination is -0.4225.

Question 50

A study was recently done in which the following regression output was generated using Excel. SUMMARY OUTPUT Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

Question 51

The following regression model has been computed based on a sample of fifty observations of part- time workers in which the individual weekly income was the dependent variable and hours worked is the independent variable : = 43.2 + 25.2x. The first observations in the sample for y and x were 350 and 15, respectively. Given this, the residual value for the first observation is approximately 71.2.

Question 52

In a simple regression model, if the regression model is deemed to be statistically significant, it means that the regression slope coefficient is significantly greater than zero.

Question 53

The sum of the residuals in a least squares regression model will be zero only when the correlation between the x and y variables is statistically significant.

Question 54

In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.04x. Given this model, for a customer with a 2,000 square foot house and a monthly utility bill equal to $100.00, the residual from the regression model is approximately -$3.40.

Question 55

In a study of 30 customers' utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately $92.00.

Question 56

If the sample value of the intercept turns out to be an illogical value, this is acceptable as long as x = 0 is not within the range of the data.

Question 57

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.

Question 58

A study was recently done in which the following regression output was generated using Excel. SUMMARY OUTPUT Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.

Question 59

If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

Question 60

The standard error of the estimate for a simple linear regression model measures the variation in the slope coefficient from sample to sample.

Question 61

When calculating prediction intervals for predicted values of y based on a given x, all 95 percent prediction intervals will be of equal width.

Question 62

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.

Question 63

In simple linear regression, the t-test for the slope and the F-test are both conducting the same hypothesis test.

Question 64

The prediction interval developed from a simple linear regression model will be at its narrowest point when the value of x used to predict y is equal to the mean value of x.

Question 65

Given the following regression equation, the predicted value for y when x = 0.5 is about 4.57

Question 66

The values of the regression coefficients are found such the sum of the residuals is minimized.

Question 67

When regression analysis is used for descriptive purposes, two of the main items of interest are whether the sign on the regression slope coefficient is positive or negative and whether the regression slope coefficient is significantly different from zero.

Question 68

A positive population slope of 12 (β1 = 12) means that a 1-unit increase in x causes an average 12-unit increase in y.

Question 69

A high coefficient of determination (R2) implies that the regression model will be a good predictor for future values of the dependent variable given the value of the independent variable.

Question 70

In a simple linear regression analysis, if the test statistic for testing the significance of the regression slope coefficient is 3.6, the F ratio from the analysis of variance table is known to be 12.96

Question 71

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: SUMMARY OUTPUT Given this output, the upper limit for the 95 percent confidence interval estimate for the true regression slope coefficient is approximately 0.28.

Question 72

A regression model that is deemed to have a regression slope coefficient that could be equal to zero should not be used for prediction since there is no established linear relationship between the x and y variable.

Question 73

When the intercept in a regression equation is deemed not significantly different from 0, then in making predictions for y, 0.0 should be used as the value of the intercept rather than the estimated intercept value.

Question 74

In analyzing the relationship between two variables, a scatter plot cannot be used to detect which of the following?

A) A positive linear relationship
B) A curvilinear relationship
C) A negative linear relationship
D) A causal relationship

Question 75

If the correlation between two variables in a simple linear regression model is calculated to be .73, the R-square value is .85.

Question 76

If a simple least squares regression model is developed based on a sample where the two variables are known to be positively correlated, the sign on the regression coefficient will be positive also.

Question 77

If the R-squared value for a regression model is high, the regression model will necessarily provide accurate forecasts of the y variable.

Question 78

If a simple least squares regression model is developed based on a sample where the two variables are known to be positively correlated, the sum of the residuals will be positive.

Question 79

State University recently randomly sampled seven students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: In testing the significance of the regression slope coefficient for the independent variable, HOURS, the calculated test statistic is approximately t = -1.47.

Question 80

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: SUMMARY OUTPUT Given this output, the point estimate for the average tip per dollar amount of the bill is approximately $0.21.