Question 1

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.Based on the output below, which of the Following statements is/are true?

$\text{ Response Variable is Sales}$

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 90.19 & 25.08 & 3.60 & 0.001 \ \text { Price } & - 0.03055 & 0.01005 & - 3.04 & 0.005 \ \text { Advertising } & 3.0926 & 0.3680 & 8.40 & 0.000 \end{array}$
$$S = 10.6075 \quad R - S q = 84.4 \% \quad R - S q ( a d j ) = 83.3 \%$$
 
$\text{Analysis of Variance}$

$\begin{array} { l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } \ \text { Regression } & 2 & 16477.3 & 8238.7 \ \text { Residual Error } & 27 & 3038.0 & 112.5 \ \text { Total } & 29 & 19515.4 & \end{array}$
A)The multiple regression model is significant overall.
B)Selling Price is a significant independent variable in explaining Bravia sales.
C)Amount Spent on Advertising is a significant independent variable in explaining Bravia sales.
D)Only A and B
E)A, B and C

Accepted Answer

The multiple regression model is significant overall, indicated by the low p-values for both Price and Advertising, showing they are significant predictors of sales. The overall model significance is also supported by the high R-squared values.

Question 2

Using the output below, calculate the predicted turnover rate for a company having a trust Index score of 70 and an average annual bonus of $6500.

$\text{ Response Variable is Turnover Rate}$

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 2.1005 & 0.7826 & 15.46 & 0.000 \ \text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \ \text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000 \end{array}$
A) $3.5 \%$
B) $4.2 \%$
C) $1.9 \%$
D) $2.4 \%$
E) None of the above.

Accepted Answer

D

Question 3

Selling price and amount spent advertising were entered into a multiple regression to
Determine what affects flat panel LCD TV sales.Use the output shown below, calculate the
Amount of variability in Sales is explained by the estimated multiple regression model.

$\text{Analysis of Variance}$
$\begin{array} { l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } \ \text { Regression } & 2 & 16477.3 & 8238.7 \ \text { Residual Error } & 27 & 3038.0 & 112.5 \ \text { Total } & 29 & 19515.4 & \end{array}$
A) $15.57 \%$
B) $6.90 \%$
C) $84.43 \%$
D) $29 \%$
E) None of the above.

Accepted Answer

The amount of variability in Sales explained by the estimated multiple regression model is calculated using the formula for R-squared ($R^2$), which is the ratio of the regression sum of squares (SS) to the total sum of squares (SS). In this case, $R^2 = \frac{16477.3}{19515.4} \approx 0.8443$ or $84.43\%$.

Question 4

A sample of 33 companies was randomly selected and data collected on the average annual
Bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).According to the
Output is shown below, what is the estimated multiple regression model? Response Variable is Turnover Rate

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \ \text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \ \text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000 \end{array}$

A) Turnover Rate $= 0.01966$ Trust Index $+ 0.0001481$ Average Bonus
B) Turnover Rate $= 0.7826 + 0.01966$ Trust Index $+ 0.0001481$ Average Bonus
C) Turnover Rate $= 12.1005 - 0.07149$ Trust Index $- 0.0007216$ Average Bonus
D) Turnover Rate $= 12.1005 + 0.07149$ Trust Index $+ 0.0007216$ Average Bonus
E) Turnover Rate $= 15.46 - 3.64$ Trust Index $- 4.87$ Average Bonus

Accepted Answer

The estimated multiple regression model is constructed by using the coefficients (Coef) from the output. The constant term is 12.1005, the coefficient for Trust Index is -0.07149, and the coefficient for Average Bonus is -0.0007216, making the correct model: Turnover Rate = 12.1005 - 0.07149 Trust Index - 0.0007216 Average Bonus.

Question 5

A sample of 33 companies was randomly selected and data collected on the average annual Bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).Using the output Below, and a significance level of ? = .01, we can conclude that

$\text{Response Variable is Turnover Rate}$

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \ \text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \ \text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000 \end{array}$
$$S = 1.49746 \quad R - S q = 79.6 \% \quad R - S q ( a d j ) = 78.3 \%$$

$\text{Analysis of Variance}$

$\begin{array} { l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } \ \text { Regression } & 2 & 262.73 & 131.36 \ \text { Residual Error } & 30 & 67.27 & 2.24 \ \text { Total } & 32 & 330.00 & \end{array}$
A)The multiple regression model is significant overall.
B)Trust Index is a significant independent variable in explaining turnover rate.
C)Average Annual Bonus is a significant independent variable in explaining turnover rate.
D)The predictor Constant is a significant independent variable in explaining turnover rate.
E)All of these.

Accepted Answer

The answer of A sample of 33 companies was randomly...

Question 6

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The regression coefficient for Price was Found to be -0.03055, which of the following is the correct interpretation for this value?
A)Increasing the price of the Sony Bravia by $100 will result in at least 3 fewer TV's sold.
B)For a given amount spent on advertising, a $100 increase in price of the Sony Bravia is associated with a decrease in sales of 3.055 units, on average.
C)Holding the amount spent on advertising constant, an increase of $100 in the price of the Sony Bravia will decrease sales by 3.055 units.
D)Holding the amount spent on advertising constant, an increase of $100 in the price of the Sony Bravia will decrease sales by .03%.
E)None of the above.

Accepted Answer

The regression coefficient of -0.03055 indicates that for every $1 increase in price, sales decrease by 0.03055 units. Therefore, for a $100 increase, sales decrease by 3.055 units, holding advertising constant.

Question 7

A sample of 33 companies was randomly selected and data collected on the average annual Bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).Based on the Output, how much of the variability in Turnover Rate is explained by the estimated multiple Regression model?

$\text{Response Variable is Turnover Rate}$

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \ \text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \ \text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000 \end{array}$

A) $ 78.3 \%$
B) $79.6 \%$
C) $12.1 \%$
D) $95.4 \%$
E) None of the above.

Accepted Answer

The R-squared value, which indicates the percentage of variability in the response variable (Turnover Rate) explained by the model, is typically provided in the regression output. In this case, it is 79.6%.

Question 8

In regression an observation has high leverage when
A)the observation has a combination of x-values that is far from the center of the data.
B)the observation is perfectly predicted by the regression.
C)the observation is poorly predicted by the regression.
D)removing the observation causes a large change in one of more coefficients of the model.
E)none of these

Accepted Answer

High leverage points in regression are observations with x-values that are far from the mean of the dataset's x-values, making them exert more influence on the slope of the regression line.

Question 9

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The plot of residuals versus predicted Values is shown below.What does the residual plot suggest? 
A)The Linearity condition is not satisfied.
B)There is an extreme departure from normality.
C)The variance is not constant.
D)The presence of a couple of outliers.
E)The plot thickens from left to right.

Accepted Answer

The answer of Selling price and amount spent advertising were...

Question 10

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. The adjusted $\mathrm { R } ^ { 2 }$ value was reported as $83.3 \%$. This means that
A) Selling price and amount spent advertising do not describe TV sales well.
B) $83.3 \%$ of the variance in TV sales can be accounted for by selling price.
C) $83.3 \%$ of the variance in TV sales can be accounted for by amount spent advertising.
D) $83.3 \%$ of the variance in TV sales can be accounted for by the model including both selling price and amount spent advertising.
E) Both selling price and amount spent advertising are significant predictors of TV sales.

Accepted Answer

The adjusted $R^2$ value of $83.3\%$ indicates that $83.3\%$ of the variance in TV sales can be explained by the regression model, which includes both selling price and amount spent on advertising. This does not necessarily mean each predictor is significant individually (without further statistical tests), but together, they account for a large portion of the variance in sales.

Question 11

Which of the following are NOT characteristics of a good regression model?
A)a relatively high
B)a relatively low value of s (the standard deviation of the residuals)
C)relatively few predictor variables
D)relatively small p-values for the F- and t-statistics
E)All of these are characteristics of a good regression model.

Accepted Answer

All the options listed (A, B, C, D) describe characteristics of a good regression model. A high $ R^2 $ indicates that the model explains a large portion of the variance in the dependent variable. A low standard deviation of the residuals (s) suggests that the model's predictions are close to the actual values. Having fewer predictor variables can make the model simpler and more interpretable, while still providing predictive power. Small p-values for the F- and t-statistics indicate that the model and its coefficients are statistically significant.

Question 12

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.Using the output below, calculated F Statistic to determine the overall significance of the estimated multiple regression model is

$\text{Analysis of Variance}$
$\begin{array} { l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } \ \text { Regression } & 2 & 16477.3 & 8238.7 \ \text { Residual Error } & 27 & 3038.0 & 112.5 \ \text { Total } & 29 & 19515.4 & \end{array}$
A) $10.61$
B) $73.23$
C) $112.5$
D) $3.60$
E) None of the above

Accepted Answer

The answer of Selling price and amount spent advertising were...

Question 13

A sample of 33 companies was randomly selected and data collected on the average annual Bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).According to the Output below, what is the F statistic to determine the overall significance of the estimated is?

$\text{Analysis of Variance}$
$\begin{array} { l r r r } \text { Source } & \text { DF } & \text { SS } & \text { MS } \ \text { Regression } & 2 & 262.73 & 131.36 \ \text { Residual Error } & 30 & 67.27 & 2.24 \ \text { Total } & 32 & 330.00 & \end{array}$

A) $58.64$
B) $1.497$
C) $131.36$
D) $78.3$
E) $2.24$

Accepted Answer

The F statistic is calculated by dividing the mean square of the regression (MSR) by the mean square of the error (MSE). From the table, MSR = 131.36 and MSE = 2.24. Therefore, F = 131.36 / 2.24 = 58.64.

Question 14

The problem of collinearity occurs when
A)there is an influential observation in the data set.
B)at least one predictor var.has a nonlinear relationship with the response variable.
C)two or more predictor variables are linearly related to each other.
D)more than one predictor variable is linearly related to the response variable.
E)none of these

Accepted Answer

The problem of collinearity occurs when two or more predictor variables are linearly related to each other, which can make it difficult to determine the individual effect of each predictor on the response variable.

Question 15

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The correct null and alternative hypotheses For testing the regression coefficient of Price is 
A)$H _ { 0 } : \beta _ { \mathrm { P } } \neq 0$ vs. $\mathrm { H } _ { \mathrm { A } } : \beta _ { \mathrm { P } } = 0$
B) $\mathrm { H } _ { 0 } : \beta _ { \mathrm { P } } \geq 0$ vs. $\mathrm { H } _ { \mathrm { A } } : \beta _ { \mathrm { P } } < 0$
C) $\mathrm { H } _ { 0 } : \beta _ { \mathrm { P } } \leq 0$ vs. $\mathrm { H } _ { \mathrm { A } } : \beta _ { \mathrm { P } } > 0$
D) $\mathrm { H } _ { 0 } : \beta _ { \mathrm { P } } = 0$ vs. $\mathrm { H } _ { \mathrm { A } } : \beta _ { \mathrm { P } } \neq 0$
E) $\mathrm { H } _ { 0 } :$ The regression is not significant vs. $\mathrm { H } _ { \mathrm { A } }$ : The regression is significant.

Accepted Answer

The correct null hypothesis ($H_0$) for testing a regression coefficient is that the coefficient is equal to zero ($\beta_P = 0$), indicating no effect. The alternative hypothesis ($H_A$) is that the coefficient is not equal to zero ($\beta_P \neq 0$), indicating an effect.

Question 16

A sample of 33 companies was randomly selected and data collected on the average annual Bonus, turnover rate (%), and trust index (measured on a scale of 0 - 100).In a multiple Regression estimating turnover rate using average bonus and trust index, what is the correct Null hypotheses for testing the regression coefficient of Trust Index?

$\text{Response Variable is Turnover Rate}$

$\begin{array} { l r r r r } \text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \ \text { Constant } & 12.1005 & 0.7826 & 15.46 & 0.000 \ \text { Trust Index } & - 0.07149 & 0.01966 & - 3.64 & 0.001 \ \text { Average Bonus } & - 0.0007216 & 0.0001481 & - 4.87 & 0.000 \end{array}$

A) $\beta { } _ { \mathrm { TI } } \neq 0$
B) $\mathrm { T } _\mathrm { TI } > 0$
C) $\beta { } _ { \mathrm { TI } } = 0$
D) $\beta { } _ { \mathrm { TI } } < 0$
E) $\mathrm { T } _ { \mathrm { TI } } \leq 0$

Accepted Answer

The correct null hypothesis for testing the regression coefficient of any predictor, including the Trust Index in this context, is that the coefficient is equal to zero ($\beta_{\text{TI}} = 0$). This hypothesis tests whether the predictor has no effect on the response variable.

Quiz 9: Multiple Regression

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The regression coefficient for Price was Found to be -0.03055, which of the following is the correct interpretation for this value?

In regression an observation has high leverage when

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The plot of residuals versus predicted Values is shown below.What does the residual plot suggest?

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. The adjusted $\mathrm { R } ^ { 2 }$ value was reported as $83.3 \%$ . This means that

Which of the following are NOT characteristics of a good regression model?

The problem of collinearity occurs when

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The correct null and alternative hypotheses For testing the regression coefficient of Price is

Quiz 9: Multiple Regression

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The regression coefficient for Price was Found to be -0.03055, which of the following is the correct interpretation for this value?

In regression an observation has high leverage when

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The plot of residuals versus predicted Values is shown below.What does the residual plot suggest?

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. The adjusted R2\mathrm { R } ^ { 2 }R2 value was reported as 83.3%83.3 \%83.3% . This means that

Which of the following are NOT characteristics of a good regression model?

The problem of collinearity occurs when

Selling price and amount spent advertising were entered into a multiple regression to Determine what affects flat panel LCD TV sales.The correct null and alternative hypotheses For testing the regression coefficient of Price is

Selling price and amount spent advertising were entered into a multiple regression to determine what affects flat panel LCD TV sales. The adjusted $\mathrm { R } ^ { 2 }$ value was reported as $83.3 \%$ . This means that