Question 1

____________ is the proportion of the variation explained by the simple linear regression model.

Accepted Answer

A) -1.2024 
B) 0.6774 
C) 37.2895 
D) 0.2934 
E) 0.2737 
A) -1.2024 
B) 0.6774 
C) 37.2895 
D) 0.2934 
E) 0.2737

Question 2

A data set with 7 observed pairs of data (x, y) yielded the following statistics. $$\sum X$$=21.57  $$\sum X ^ { 2 }$$=68.31  $$\sum Y$$ =188.9 $$\sum Y ^ { 2 }$$ =5140.23 $$\sum X Y$$ =590.83 
SSE = unexplained variation = 1.06
-What is the value of SSxy?

Accepted Answer

A) 7.368 
B) 8.748 
C) 1.844 
D) 4.745 
E) 5.140 
A) 7.368 
B) 8.748 
C) 1.844 
D) 4.745 
E) 5.140

Question 3

A local grocery store wants to predict the daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/Mega-Stat output given below summarizes the results of fitting a simple linear regression model using this data.
Regression Analysis
$\begin{array}{rc}
\mathrm{r}^{2} 0.762 & \mathrm{n} 7 \
\mathrm{R} 0.873 & \mathrm{k} \text { 1 } \
\text { Std. Error 11.547 } & \text { Dep. Var. Sales }
\end{array}$
ANOVA
table
$\begin{array}{rrrrrr}
\hline \text { Source } & S S & d f & M S & F & p \text {-value } \
\hline \text { Regression } & 2,133.3333 & 1 & 2,133.3333 & 16.00 & .0103 \
\text { Residual } & 666.6667 & 5 & 133.3333 & & \
\hline \text { Total } & 2,800.0000 & 6 & & &\\hline
\end{array}$

$\text { Regression output }$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Confidence interval }$
$\begin{array}{rrrrrrrr}
\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \
& & & & & \text { lower } & \
\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \
\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &
\end{array}$
-In testing the simple linear regression equation for significance at a significance level of 0.05,what is the critical value for the F test?

Accepted Answer

A) 16.26 
B) 10.01 
C) 6.61 
D) 230.2 
E) 5.79 
A) 16.26 
B) 10.01 
C) 6.61 
D) 230.2 
E) 5.79

Question 4

In a simple regression analysis for a given data set,if the null hypothesis H0: $\beta _ { 1 }$
= 0 is rejected,then the null hypothesis H0: $\rho$
= 0 is _____ rejected.

Accepted Answer

A) also 
B) not 
C) sometimes 
D) Cannot be determined without more information. 
A) also 
B) not 
C) sometimes 
D) Cannot be determined without more information.

Question 5

A local tire dealer wants to predict the number of tires sold each month.The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising.The dealer randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires)and monthly advertising expenditures (in thousands of dollars).The simple linear regression equation is $\hat { y }$ 
= 3 + 1x.The dealer randomly selects one of the six observations with a monthly sales value of 8000 tires and monthly advertising expenditures of $7000.Calculate the value of the residual for this observation.

Accepted Answer

-2 @#IMG-DLM& 
= 3 +

Question 6

The 95% confidence interval for the slope is from .564 to 1.436.Interpret this confidence interval.

Accepted Answer

We are 95% confident that if t

Question 7

The sample correlation coefficient is the ratio of explained variation to total variation.

Accepted Answer

A) True 
 B)False

Question 8

Consider the following partial computer output from a simple linear regression analysis. $$\begin{array} { l c c c c } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 67.05 & 20.90 & 3.21 & 0.012 \
\text { Independent Var } & 5.8167 & 0.7085 & \_\_\_& 0.000
\end{array}$$ S = _________ R-Sq = _______
Analysis of Variance $$\begin{array} { l c c c c c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & - & 34920 & 67.39 & 0.000 \
\text { Residual Error } & 8 & - & 518 & & \
\text { Total } & 9 & 39065 & & &
\end{array}$$
-What is the unexplained variance?

Accepted Answer

The answer of Consider the following partial computer output from...

Question 9

Test to determine if there is a significant correlation between x and y Use H0: ? = 0 versus Ha: ? ? 0 by setting $\alpha$ 
= .01
Reject the null hypothesis,there is a significant correlation between x and y

Accepted Answer

r = .945,then
t = (.945*?8)/(?

Question 10

A local tire dealer wants to predict the number of tires sold each month. The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising. The dealer randomly selects 6 months of data consisting of monthly tire sales (in thousands of tires) and monthly advertising expenditures (in thousands of dollars). Residuals are calculated for all of the randomly selected six months and ordered from smallest to largest.
-Determine the normal score for the smallest residual.

Accepted Answer

The answer of A local tire dealer wants to predict...

Question 11

In a simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

Accepted Answer

A) True 
 B)False

Question 12

The least-squares regression line minimizes the sum of the:

Accepted Answer

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 
E) Squared differences between actual and predicted X values 
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 
E) Squared differences between actual and predicted X values

Question 13

Consider the following partial computer output from a simple linear regression analysis: $$\begin{array} { l l c c c } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \
\text { Constant } & 5566.1 & 254.0 & 21.91 & 0.000 \
\text { Independent Var } & - 210.35 & 24.19 & - &
\end{array}$$ S = _________ R-Sq =
Analysis of Variance $\begin{array}{lccrcc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & 3963719 & 3963719 & 75.59 & 0.000 \
\text { Residual Error } & 14 &\_\_\_ & 52439 & &\
\text { Total }&15&\_\_\_
\end{array}$
-What is the correlation coefficient?

Accepted Answer

r = -?.843

Question 14

Consider the following partial computer output from a simple linear regression analysis: $$\begin{array} { l l c c c } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \
\text { Constant } & 5566.1 & 254.0 & 21.91 & 0.000 \
\text { Independent Var } & - 210.35 & 24.19 & - &
\end{array}$$ S = _________ R-Sq =
Analysis of Variance $\begin{array}{lccrcc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & 3963719 & 3963719 & 75.59 & 0.000 \
\text { Residual Error } & 14 &\_\_\_ & 52439 & &\
\text { Total }&15&\_\_\_
\end{array}$
-What is the unexplained variation?

Accepted Answer

The answer of Consider the following partial computer output from...

Question 15

A data set with 7 observations yielded the following.Use the simple linear regression model where y is the dependent variable and x is the independent variable. $\sum x$ = 21.57 $\sum X ^ { 2 }$ = 68.31 $\sum Y ^ { 2 }$ = 188.9 $\sum Y ^ { 2 }$ = 5,140.23 $\sum X Y$ = 590.83
SSE = 1.06
-Find the estimated slope.

Accepted Answer

The answer of A data set with 7 observations yielded...

Question 16

The notation $\hat { y }$ 
is the population average value of the dependent variable y.

Accepted Answer

A) True 
 B)False

Question 17

Consider the following partial computer output from a simple linear regression analysis. $$\begin{array} { l c c c c } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \text { T } & \text { P } \
\text { Constant } & 67.05 & 20.90 & 3.21 & 0.012 \
\text { Independent Var } & 5.8167 & 0.7085 & \_\_\_& 0.000
\end{array}$$ S = _________ R-Sq = _______
Analysis of Variance $$\begin{array} { l c c c c c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & - & 34920 & 67.39 & 0.000 \
\text { Residual Error } & 8 & - & 518 & & \
\text { Total } & 9 & 39065 & & &
\end{array}$$
-Write the equation of the least squares line.

Accepted Answer

The answer of Consider the following partial computer output from...

Question 18

A local tire dealer wants to predict the number of tires sold each month.The dealer believes that the number of tires sold is a linear function of the amount of money invested in advertising.The dealer randomly selects 6 months of data consisting of tire sales (in thousands of tires)and advertising expenditures (in thousands of dollars).Based on the data set with 6 observations,the simple linear regression model yielded the following results. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196
-Find the rejection point for the t statistic at a = .05 and test H0: ?1? 0 vs.Ha: b1> 0.

Accepted Answer

t = 2.645,

Question 19

Consider the following partial computer output from a simple linear regression analysis: $$\begin{array} { l l c c c } 
\text { Predictor } & \text { Coef } & \text { SE Coef } & \mathrm { T } & \mathrm { P } \
\text { Constant } & 5566.1 & 254.0 & 21.91 & 0.000 \
\text { Independent Var } & - 210.35 & 24.19 & - &
\end{array}$$ S = _________ R-Sq =
Analysis of Variance $\begin{array}{lccrcc}
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & 3963719 & 3963719 & 75.59 & 0.000 \
\text { Residual Error } & 14 &\_\_\_ & 52439 & &\
\text { Total }&15&\_\_\_
\end{array}$
-What is the total variation?

Accepted Answer

Total variation = Ex

Question 20

-Calculate the SSE

Accepted Answer

SSE = MSE

____________ is the proportion of the variation explained by the simple linear regression model.

A data set with 7 observed pairs of data (x, y) yielded the following statistics. $\sum X$ =21.57 $\sum X ^ { 2 }$ =68.31 $\sum Y$ =188.9 $\sum Y ^ { 2 }$ =5140.23 $\sum X Y$ =590.83 SSE = unexplained variation = 1.06 -What is the value of SSxy?

In a simple regression analysis for a given data set,if the null hypothesis H₀: $\beta _ { 1 }$ = 0 is rejected,then the null hypothesis H₀: $\rho$ = 0 is _____ rejected.

The 95% confidence interval for the slope is from .564 to 1.436.Interpret this confidence interval.

The sample correlation coefficient is the ratio of explained variation to total variation.

Test to determine if there is a significant correlation between x and y Use H₀: ? = 0 versus H_a: ? ? 0 by setting $\alpha$ = .01 Reject the null hypothesis,there is a significant correlation between x and y

In a simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

The least-squares regression line minimizes the sum of the:

The notation $\hat { y }$ is the population average value of the dependent variable y.

-Calculate the SSE

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

Exam 11: Correlation Coefficient and Simple Linear Regression Analysis

____________ is the proportion of the variation explained by the simple linear regression model.

A data set with 7 observed pairs of data (x, y) yielded the following statistics. ∑X\sum X∑X =21.57 ∑X2\sum X ^ { 2 }∑X2 =68.31 ∑Y\sum Y∑Y =188.9 ∑Y2\sum Y ^ { 2 }∑Y2 =5140.23 ∑XY\sum X Y∑XY =590.83 SSE = unexplained variation = 1.06 -What is the value of SSxy?

In a simple regression analysis for a given data set,if the null hypothesis H0: β1\beta _ { 1 }β1​ = 0 is rejected,then the null hypothesis H0: ρ\rhoρ = 0 is _____ rejected.

The 95% confidence interval for the slope is from .564 to 1.436.Interpret this confidence interval.

The sample correlation coefficient is the ratio of explained variation to total variation.

Test to determine if there is a significant correlation between x and y Use H0: ? = 0 versus Ha: ? ? 0 by setting α\alphaα = .01 Reject the null hypothesis,there is a significant correlation between x and y

In a simple linear regression analysis,we assume that the variance of the independent variable (X)is equal to the variance of the dependent variable (Y).

The least-squares regression line minimizes the sum of the:

The notation y^\hat { y }y^​ is the population average value of the dependent variable y.

-Calculate the SSE

An Introduction to Business Statistics

Descriptive Statistics

Probability

Discrete Random Variables

Continuous Random Variables

Sampling Distributions

Confidence Intervals

Hypothesis Testing

Statistical Inferences Based on Two Samples

Experimental Design and Analysis of Variance

Multiple Regression and Model Building

Nonparametric Methods

Chi-Square Tests

Decision Theory

Time Series Forecasting

Filters

A data set with 7 observed pairs of data (x, y) yielded the following statistics. $\sum X$ =21.57 $\sum X ^ { 2 }$ =68.31 $\sum Y$ =188.9 $\sum Y ^ { 2 }$ =5140.23 $\sum X Y$ =590.83 SSE = unexplained variation = 1.06 -What is the value of SSxy?

In a simple regression analysis for a given data set,if the null hypothesis H₀: $\beta _ { 1 }$ = 0 is rejected,then the null hypothesis H₀: $\rho$ = 0 is _____ rejected.

Test to determine if there is a significant correlation between x and y Use H₀: ? = 0 versus H_a: ? ? 0 by setting $\alpha$ = .01 Reject the null hypothesis,there is a significant correlation between x and y

The notation $\hat { y }$ is the population average value of the dependent variable y.