Deck 7: Advanced Regression Analysis

Question 1

In a regression model, the __________ exists when a predictor variable has a different partial effect on the outcome of another predictor variable.

A) target effect
B) interaction effect
C) dummy effect
D) predictor effect

Answer 1

interaction effect

Question 2

What is the predicted value ( $\hat{y}$ ) when the numerical variable is x = 70 for the regression equation $\hat{y}$ = ?831 + 29.0x ? 0.113x²?

A) 1,967.7
B) 1,454.2
C) 645.3
D) Not enough sufficient data to calculate the predicted value.

Answer 2

645.3

Question 3

What is the predicted value ( $\hat{y}$ ) when the numerical variable is x = 70 for the regression equation $\hat{y}$ = -810 + 24.4x - 0.142x²?

A) 1822.2
B) 1593.8
C) 202.2
D) Not enough sufficient data to calculate the predicted value.

Answer 3

202.2

Question 4

A variable with a value of x₁x₂ is added to the general linear regression model to account for two predictive variables, x₁ and x₂ and the effect on the response variable. This type of effect is called __________.

A) transformative
B) dummy
C) interaction
D) predictive

Question 5

Consider the sample correlation coefficients in the table below. How much of the variability in time can be explained by boxes using the alternative way of to determine the coefficient of determination.

A) 79%
B) 26.0%
C) 49.4%
D) 57.0%

Question 6

Consider the sample correlation coefficients in the table below. How much of the variability in time can be explained by boxes using the alternative way of to determine the coefficient of determination.

A) 75%
B) 25.5%
C) 49.5%
D) 55.6%

Question 7

A study was completed on cholesterol in 100 male adults 40-60 years of age to determine if there is a relationship between cholesterol concentration and time spent watching TV. The researchers wanted to determine if there are any predictive results, such as if the amount of time spent watching TV increases or decreases cholesterol levels. Based on the following regression results, what was the overall study p-value and is it statistically significant?

A) The p-value = 0.002 and is statistically significant because it is under the 5% level.
B) The p-value = 0.002 and is not statistically significant because it is under the 5% level.
C) The p-value = 0.000 and is statistically significant because it is under the 5% level.
D) The p-value = 0.001 and is statistically significant because it is under the 5% level.

Question 8

A study was completed on cholesterol in 100 male adults 40-60 years of age to determine if there is a relationship between cholesterol concentration and time spent watching TV. The researchers wanted to determine if there are any predictive results, such as if the amount of time spent watching TV increases or decreases cholesterol levels. Based on the following regression results, what was the overall study p-value and is it statistically significant?

A) The p-value = 0.003 and is statistically significant because it is under the 5% level.
B) The p-value = 0.003 and is not statistically significant because it is under the 5% level.
C) The p-value = 0.000 and is statistically significant because it is under the 5% level.
D) The p-value = 0.002 and is statistically significant because it is under the 5% level.

Question 9

Consider a linear regression model where y represents the response variable and d₁ and d₂ represent two dummy variables. The model is estimated as $\hat{y}$ = -2.49 + 1.86x + 3.20d₁ - 2.21d₂ + 0.50d₁d₂. Compute $\hat{y}$ for x = 3, d₁ = 1, and d₂ = 0.

A) 13.61
B) 3.42
C) 13.17
D) 6.29

Question 10

Consider a linear regression model where y represents the response variable and d₁ and d₂ represent two dummy variables. The model is estimated as $\hat{y}$ = -2.53 + 2.04x + 4.20d₁ - 2.86d₂ + 0.68d₁d₂. Compute $\hat{y}$ for x = 3, d₁ = 1, and d₂ = 0.

A) 13.53
B) 3.71
C) 12.85
D) 7.79

Question 11

Sam, a marketing manager for XYZ big box stores, is trying to determine if there is a relationship between shelf space (in feet) and sales (in hundreds of dollars). To do this, Sam selected the top 12 producing locations. The regression results produced the following adjusted R² values: Model 1: 0.8874 and Model 2: 0.6028. Which model is more suitable of a prediction?

A) Model 1
B) Model 2
C) Both are suitable
D) Neither model

Question 12

Sam, a marketing manager for XYZ big box stores, is trying to determine if there is a relationship between shelf space (in feet) and sales (in hundreds of dollars). To do this, Sam selected the top 12 producing locations. Using the provided Model 1 results, what is the estimated equation on Sales?

A) ^Sales = 10.085 + 0.203shelves + 0.074shelf_space
B) ^Sales = -0.203shelves + 0.074shelf_space
C) ^Sales = 0.203shelves + 0.074shelf_space
D) ^Sales = 0.074shelf_space ÷ (2 × 0.203shelves)

Question 13

Sam, a marketing manager for XYZ big box stores, is trying to determine if there is a relationship between shelf space (in feet) and sales (in hundreds of dollars). To do this, Sam selected the top 12 producing locations. Using the provided Model 1 results, what is the estimated equation on Sales?

A) ^Sales = 10.365 + 0.211shelves + 0.074shelf_space
B) ^Sales = -0.211shelves + 0.074shelf_space
C) ^Sales = 0.211shelves + 0.074shelf_space
D) ^Sales = 0.074shelf_space ÷ (2 × 0.211shelves)

Question 14

Sam, a marketing manager for XYZ big box stores, is trying to determine if there is a relationship between shelf space (in feet) and sales (in hundreds of dollars). To do this, Sam selected the top 12 producing locations. Using the provided Model 1 results, which option best interprets the impact of the coefficients and p-values?

^* the p-value

A) The predictor variables are below one offering a negative correlation.
B) All predictor variables are positive with a significant influence on sales.
C) There is no impact presented with the coefficients and p-value results.
D) The p-value offers significant influence where the coefficient provides reduction on sales.

Question 15

The estimate regression equation for the average cost of widgets is:
^Widgets = 7.33 - 0.2340 Output + 0.1892 Output². Both predictor variables are statistically significant at 5% level, confirming the quadratic effect. What is the predictive average from an output level of 2 million units to 3 million units?

A) The increase in output units results in a $0.02 decrease in predictive average cost.
B) The increase in output units results in a $0.24 increase in predictive average cost.
C) The increase in output units results in a $0.71 decrease in predictive average cost.
D) The increase in output units results in a $0.71 increase in predictive average cost.

Question 16

The estimate regression equation for the average cost of widgets is:
^Widgets = 7.23 - 0.2478 Output + 0.1954 Output². Both predictor variables are statistically significant at 5% level, confirming the quadratic effect. What is the predictive average from an output level of 2 million units to 3 million units?

A) The increase in output units results in a $0.02 decrease in predictive average cost.
B) The increase in output units results in a $0.24 increase in predictive average cost.
C) The increase in output units results in a $0.73 decrease in predictive average cost.
D) The increase in output units results in a $0.73 increase in predictive average cost.

Question 17

Todd uses the quadratic regression model to determine the predictive average unit cost of baseballs produced in his production facility. After determining predictive average costs at multiple unit batch size amounts in millions, he now wants to know what the output level that minimizes his costs would be.

-Given b₁ = -0.3600 and b₂ = 0.0201, what is the level that will maximize his average cost in units?

A) 7.6 million units
B) 3.3 million units
C) 18.80 million units
D) 8.96 million units

Question 18

Todd uses the quadratic regression model to determine the predictive average unit cost of baseballs produced in his production facility. After determining predictive average costs at multiple unit batch size amounts in millions, he now wants to know what the output level that minimizes his costs would be.

- Given b₁ = ?0.3802 and b₂ = 0.0198, what is the level that will maximize his average cost in units?

A) 7.5 million units
B) 3.7 million units
C) 19.20 million units
D) 9.60 million units

Question 19

Ava Diego, a doctoral student, is researching car loans issued at a local bank. She prepared a sample of 200 to determine if there is a relationship between the loan amount, length of the loan, and interest rate provided. The regression results are in the table below. Which model is more suitable for prediction and what is the best fit reason?

A) Model 2 is the most suitable because of the p-value variance.
B) Model 1 is the most suitable because of the higher adjusted R² value.
C) Model 2 is the most suitable because of the lower adjusted R² value.
D) Neither provide enough results data to predict the model or reasoning.

Question 20

An estimated linear regression of annual fuel expenditures y on annual income x is represented as the following equation: $\hat{y}$ = 2,700 + 0.02x. What is the estimated slope coefficient value?

A) 0.02
B) 2b1 + 0.02
C) 54
D) 54x

Question 21

An estimated linear regression of annual fuel expenditures y on annual income x is represented as the following equation: y= 2,200 + 0.05x. What is the estimated slope coefficient value?

A) 0.05
B) 2b₁ + 0.05
C) 110
D) 110x

Question 22

An estimated linear regression of annual fuel expenditures y on annual income x is represented as the following equation: y= 2,200 + 0.05x. Jim was offered a new job that would increase his salary by $2,000. What would be his potential increase in fuel costs? Based on this information, is the assumption of increased fuel cost against annual salary meaningful?

A) The increase in fuel cost is $100.00 annually; linearity assumption is justified.
B) The increase in fuel cost is $100.00 annually; linearity assumption is not justified.
C) The increase in fuel cost is $50.00 annually; linearity assumption is justified.
D) The increase in fuel cost is $1000.00 annually; linearity assumption is not justified.

Question 23

In the following logarithmic regression model, $\beta$ ₁ × 0.01 measures the approximate unit change in E(y) when x increases. If $\beta$ ₁ = 11,500, then what is the unit change in E(y)?

A) 11.5 units
B) 1,150 units
C) 115 units
D) 11,500 units

Question 24

In the following logarithmic regression model, $\beta$ ₁ × 0.01 measures the approximate unit change in E(y) when x increases. If $\beta$ ₁ = 6,000, then what is the unit change in E(y)?

A) 6 units
B) 600 units
C) 60 units
D) 6,000 units

Question 25

In an exponential regression model, the exact percentage of change can be calculated as: (exp( $\beta$ ₁) - 1) × 100. If $\beta$ ₁ = 0.23, what is the percent increase in E(y)?

A) 25%
B) 26%
C) 75%
D) 22%

Question 26

In an exponential regression model, the exact percentage of change can be calculated as: (exp( $\beta$ ₁) - 1) × 100. If $\beta$ ₁ = 0.25, what is the percent increase in E(y)?

A) 25%
B) 28%
C) 75%
D) 22%

Question 27

In the model y = $\beta$ ₀ + $\beta$ ₁ln(x) + $\varepsilon$ , the predicted value is = b₀ + b₁ln(x). What is the impact of the estimated slope coefficient?

A) b₁ measures the approximate change in when x increases by 1 unit.
B) b₁ × 0.01 measures the approximate change in when x increases by 1%.
C) b1 measures the approximate change in when x increases by 1%.
D) b₁ × 100 measures the approximate change in when x increases by 1 unit.

Question 28

In the model y = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ , the predicted value is = b₀ + b₁x. What is the impact of the estimated slope coefficient?

A) b1 measures the approximate change in when x increases by 1 unit.
B) b₁ × 0.01 measures the approximate change in when x increases by 1%.
C) b1 measures the approximate change in when x increases by 1%.
D) b₁ × 100 measures the approximate change in when x increases by 1 unit.

Question 29

In the model ln(y) = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ , the predicted value is = exp (b₀ + b₁x + ÷ 2). What is the impact of the estimated slope coefficient?

A) b1 measures the approximate change in when x increases by 1 unit.
B) b₁ × 0.01 measures the approximate change in when x increases by 1%.
C) b1 measures the approximate change in when x increases by 1%.
D) b₁ × 100 measures the approximate change in when x increases by 1 unit.

Question 30

Consider the following quadratic model, y^= 30 + 1.50x ? 0.25x². Predict y when x = 14.

A) 2
B) 40
C) 12
D) 9

Question 31

<p>Consider the following quadratic model, = 25 + 1.5x ? 0.25x². Predict y when x = 12.

A) 40
B) 12
C) 9
D) 7

Question 32

Consider a binary response variable y and a predictor variable x that varies between 0 and 5. The linear model is estimated as = -2.90 + 0.65x. What is the estimated probability for x = 5?

A) 0.35
B) 6.15
C) 0.65
D) -6.15

Question 33

Christian Za is using the holdout method to partition his data into two independent and mutually exclusive sets: 75% in a training set and 25% in a validation set. Based on an R² value of 0.4532 and RMSE of 0.3268 for the training set and an R² value of 0.1426 and RMSE of 0.5371 for the validation set, which of the competing models is the preferred model?

A) The validation data set would be the preferred model.
B) The training data set would be the preferred model.
C) Both models are preferred models.
D) There is not enough data to determine the preferred model.

Question 34

Using a sample of 50, the following regression output is obtained from estimating the linear probability regression model y = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ . What is the predicted probability when x = 14?

A) 4.42
B) 143.90
C) 3.86
D) 0.72

Question 35

Using a sample of 50, the following regression output is obtained from estimating the linear probability regression model y = $\beta$ ₀ + $\beta$ ₁x + $\varepsilon$ . What is the predicted probability when x = 14?

A) 4.42
B) 3.86
C) 8.34
D) 0.72

Question 36

The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x₁ and x₂, what is the predicted probability implied by the logistic regression model for x₁ = 2 with x₂ = 15? (Hint: for logit, the model is $\hat{y}$ = exp(b0+ b1x1 + b2x2)1 + exp(b0 + b1x1 + b2x2).exp(b0+ b1x1 + b2x21 + expb0 + b1x1 + b2x2.)

A) 0.006
B) 0.085
C) -5.160
D) 0.005

Question 37

The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x₁ and x₂, what is the predicted probability implied by the logistic regression model for x₁ = 2 with x₂ = 15? (Hint: for logit, the model is $\hat{y}$ = ) < / p >

A) 0.838
B) 0.006
C) -5.16
D) 0.005

Question 38

The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x₁ and x₂, What is the estimated linear probability implied by the logistic probability regression model for x₁ = 3 with x₂ = 9?

A) 1.87
B) 0.35
C) 0.64
D) -0.87

Question 39

The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x₁ and x₂, What is theestimated linear probabilityimplied by the logistic probability regression model for x₁ = 3 with x₂ = 9?

A) 1.87
B) -0.35
C) 0.35
D) -0.87

Question 40

A regression model made to conform to a sample set of data, compromising predictive power is called __________.

A) cross-validation
B) flooding
C) overfitting
D) binary choice

Question 41

A linear regression model applied to a binary response variable is called a __________.

A) logistic regression model
B) log-transformed model
C) log-log regression model
D) linear probability regression model

Question 42

Which interpretation of a linear probability regression model represents the estimate ^P = -40 + 0.05x?

A) for each 1 unit increase in x, the predicted probability ^P decreases by 0.05.
B) for each 40 unit decrease in x, the predicted probability ^P increases by 40.
C) for each 1 unit increase in x, the predicted probability ^P increases by 0.05.
D) for each 0.05 unit increase in x, the predicted probability ^P decreases by 40.

Question 43

In cross-validation, if k equals the sample size, the resulting method is also called __________.

A) sensitive data cross-validation method
B) the leave-one-out cross-validation method
C) equality cross-validation method
D) partition cross-validation method

Question 44

In using both the linear probability regression and the logistic regression models for n = 40, the following table is the analysis of the holdout method. Based on the table, what is the impact of changing the $\hat{y}$ to binary predictions?

A) There is no relevant outcome changing ? to a binary variable.
B) By comparing $\hat{y}$ to y, the validation results are not able to be validated.
C) By comparing $\hat{y}$ to y, the accuracy of the model is 100%, but can change with a larger validation set.
D) By comparing $\hat{y}$ to y, the accuracy of the model is 100% and will not change based on a larger validation set.

Question 45

In determining the partial effect on dummy variable d in a regression model with an interaction variable $\hat{y}$ = b₀ + b₁x + b₂d + b₃xd, the numeric variable x value needs to be known.

Question 46

In a regression model with two dummy variables and an interaction variable d₁d₂:y = $\beta$ ₀ + $\beta$ ₁d₁ + $\beta$ ₂d₂ + $\beta$ ₃d₁d₂ + $\varepsilon$ , the interaction variables are easy to estimate.

Question 47

In the quadratic regression model, if $\beta$ ₂ > 0 then the relationship between x and y is an inverted U-shape.

Question 48

ln(y) = $\beta$ ₀ + $\beta$ ₁ ln(x) + $\varepsilon$ represents the exponential regression model.

Question 49

In the linear probability regression model, the response variable y will equal 1 or 0 to represent the probability of success.

Question 50

To test for the accuracy rate in a binary choice model, the number of correct classification observations for both outcomes should be reported.

Question 51

In the k-fold cross-validation method, the smaller the k value, the greater the reliability of the k-fold method.

Question 52

Because software packages use random draws of the observations to partition data, the results will not be identical to a fixed partitioning of the observations.