Question 1

-Calculate the MSE.

Accepted Answer

MSE = s² =

Question 2

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 }$
$\begin{array}{rrrrrrrr}
\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \
& & & & & \text { lower } & \
\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \
\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &
\end{array}$
-At a significance level of 0.05,use an F test to test the significance of the slope and state your conclusion.

Accepted Answer

A) We reject H0and conclude there is sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
B) We failed to reject H0and conclude there is not sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
C) We failed to reject H0and conclude there is sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
D) We fail to reject H0and conclude that there is sufficient evidence that grocery store sales in dollars is a significant linear predictor of the dollars spent on advertising. 
E) We reject H0and conclude that there is not sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
A) We reject H0and conclude there is sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
B) We failed to reject H0and conclude there is not sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
C) We failed to reject H0and conclude there is sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales. 
D) We fail to reject H0and conclude that there is sufficient evidence that grocery store sales in dollars is a significant linear predictor of the dollars spent on advertising. 
E) We reject H0and conclude that there is not sufficient evidence that dollars spent on advertising is a significant linear predictor of the grocery store sales.

Question 3

The error term in a simple linear regression model is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

Accepted Answer

A) True 
 B)False

Question 4

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 $$\begin{array} { l c c c c c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P } \
\text { Regression } & 1 & - & 34920 & 67.39 & 0.000 \
\text { Residual Error } & 8 & - & 518 & & \
\text { Total } & 9 & 39065 & & &
\end{array}$$
-Calculate the standard error of the model.

Accepted Answer

s = ?MSE =

Question 5

A sample correlation coefficient of 0.22 was found between outdoor temperatures and unexcused absences at a construction site.What can the HR director conclude?

Accepted Answer

A) 48.4% of the absences can be predicted by the outdoor temperature 
B) 0.48% of the absences can be predicted by the outdoor temperature 
C) 0.22% of the absences can be predicted by the outdoor temperature 
D) 4.84% of the absences can be predicted by the outdoor temperature 
E) 22.0% of the absences can be predicted by the outdoor temperature 
A) 48.4% of the absences can be predicted by the outdoor temperature 
B) 0.48% of the absences can be predicted by the outdoor temperature 
C) 0.22% of the absences can be predicted by the outdoor temperature 
D) 4.84% of the absences can be predicted by the outdoor temperature 
E) 22.0% of the absences can be predicted by the outdoor temperature

Question 6

All of the following are assumptions of the error terms in the simple linear regression model except:

Accepted Answer

A) Errors are normally distributed. 
B) Error terms have a mean of zero. 
C) Error terms have a constant variance. 
D) Error terms indicate a positive autocorrelation. 
E) Error terms are statistically independent. 
A) Errors are normally distributed. 
B) Error terms have a mean of zero. 
C) Error terms have a constant variance. 
D) Error terms indicate a positive autocorrelation. 
E) Error terms are statistically independent.

Question 7

After plotting the data points on a scatter plot,we observe that as x increases y tends to decrease in an approximately linear fashion.Therefore,we can expect the sign of both the estimated slope and the sample correlation coefficient to be ______.

Accepted Answer

The answer of After plotting the data points on a...

Question 8

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Partial results based on a sample of 10 metal sheets are given below.The simple linear regression equation is $\hat { y }$ = 1 + 1x .The time is in minutes and the strength is measured in g/cmS1U1P12S1S1P0.You are also given the following sample statistics:
MSE = 0.5, $\sum X$ = 30, $\sum X ^ { 2 }$ = 104.
-Predict the strength when heating time is 3 minutes.

Accepted Answer

5 @#IMG-DLM& 
= 1 +

Question 9

In a simple linear regression model,for any value of the dependent variable was assume that the error term have a mean equal to ____________.

Accepted Answer

The answer of In a simple linear regression model,for any...

Question 10

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
-Calculate the coefficient of determination.

Accepted Answer

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

Question 11

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 equation of the least squares line is $\hat { y }$ = 3 + 1x. $\sum X$ = 24 $\sum X ^ { 2 }$ = 124 $\sum Y$ = 42 $\sum Y ^ { 2 }$ = 338 $\sum X Y$ = 196
MSE = 4
-Using the sums of the squares given above,determine the 95% confidence interval for the slope.

Accepted Answer

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

Question 12

After plotting the data points on a scatter plot,we have observed an inverse relationship between the independent variable (x)and the dependent variable (y).Therefore,we can expect both the sample _____ and the sample _____________ to be negative values.

Accepted Answer

A) intercept,slope 
B) slope,coefficient of determination 
C) intercept,correlation coefficient 
D) slope,correlation coefficient 
E) slope,standard error of estimate 
A) intercept,slope 
B) slope,coefficient of determination 
C) intercept,correlation coefficient 
D) slope,correlation coefficient 
E) slope,standard error of estimate

Question 13

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
-Determine unexplained variation sum of squares (SSE),the explained variation sum of squares (SSR),and the total variation sum of squares (SST).

Accepted Answer

SSE = 16,S

Question 14

If one of the assumptions of the regression model is violated,performing a _______ on the dependent variable can remedy the situation.

Accepted Answer

The answer of If one of the assumptions of the...

Question 15

A simple linear regression analysis based on 12 observations yielded the following results: $\hat { y }$
= 34.2895 - 1.2024x,r2 = 0.6744, $s _ { b _ { 1 } }$
= 0)2934.
What is the t-statistic for testing whether or not there is a linear relationship between the independent and dependent variables?

Accepted Answer

A) 4.90 
B) 1.81 
C) -2.93 
D) 1.20 
E) -4.10 
A) 4.90 
B) 1.81 
C) -2.93 
D) 1.20 
E) -4.10

Question 16

An experiment was performed on a certain metal to determine if the strength is a function of heating time.Results based on 10 metal sheets are given below.Use the simple linear regression model. $\sum X$ = 30 $\sum X ^ { 2 }$ = 104 $\sum Y$ = 40 $\sum Y ^ { 2 }$ = 178 $\sum X Y$ = 134
-Determine unexplained variation sum of squares (SSE),the explained variation sum of squares (SSR),and the total variation sum of squares (SST).

Accepted Answer

SSE = 4,SS

Question 17

If r = -1,then we can conclude that there is a perfect linear relationship between the dependent and independent variables.

Accepted Answer

A) True 
 B)False

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
-What is the value of the total sum of squares,or total variation?

Accepted Answer

A) 24 
B) 28 
C) 44 
D) 16 
E) 6 
A) 24 
B) 28 
C) 44 
D) 16 
E) 6

Question 19

The least-squares point estimates of the simple linear regression model minimize the _____.

Accepted Answer

SSE or sum

Question 20

The sample correlation coefficient may assume any value between:

Accepted Answer

A) 0 and 1 
B) -× and × 
C) 0 and 8 
D) -1 and 1 
E) -1 and 0 
A) 0 and 1 
B) -× and × 
C) 0 and 8 
D) -1 and 1 
E) -1 and 0

-Calculate the MSE.

The error term in a simple linear regression model is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

A sample correlation coefficient of 0.22 was found between outdoor temperatures and unexcused absences at a construction site.What can the HR director conclude?

All of the following are assumptions of the error terms in the simple linear regression model except:

After plotting the data points on a scatter plot,we observe that as x increases y tends to decrease in an approximately linear fashion.Therefore,we can expect the sign of both the estimated slope and the sample correlation coefficient to be ______.

In a simple linear regression model,for any value of the dependent variable was assume that the error term have a mean equal to ____________.

After plotting the data points on a scatter plot,we have observed an inverse relationship between the independent variable (x)and the dependent variable (y).Therefore,we can expect both the sample _ and the sample _________ to be negative values.

If one of the assumptions of the regression model is violated,performing a _______ on the dependent variable can remedy the situation.

A simple linear regression analysis based on 12 observations yielded the following results: $\hat { y }$ = 34.2895 - 1.2024x,r² = 0.6744, $s _ { b _ { 1 } }$ = 0)2934. What is the t-statistic for testing whether or not there is a linear relationship between the independent and dependent variables?

If r = -1,then we can conclude that there is a perfect linear relationship between the dependent and independent variables.

The least-squares point estimates of the simple linear regression model minimize the _____.

The sample correlation coefficient may assume any value between:

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

-Calculate the MSE.

The error term in a simple linear regression model is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

A sample correlation coefficient of 0.22 was found between outdoor temperatures and unexcused absences at a construction site.What can the HR director conclude?

All of the following are assumptions of the error terms in the simple linear regression model except:

After plotting the data points on a scatter plot,we observe that as x increases y tends to decrease in an approximately linear fashion.Therefore,we can expect the sign of both the estimated slope and the sample correlation coefficient to be ______.

In a simple linear regression model,for any value of the dependent variable was assume that the error term have a mean equal to ____________.

After plotting the data points on a scatter plot,we have observed an inverse relationship between the independent variable (x)and the dependent variable (y).Therefore,we can expect both the sample _____ and the sample _____________ to be negative values.

If one of the assumptions of the regression model is violated,performing a _______ on the dependent variable can remedy the situation.

If r = -1,then we can conclude that there is a perfect linear relationship between the dependent and independent variables.

The least-squares point estimates of the simple linear regression model minimize the _____.

The sample correlation coefficient may assume any value between:

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

After plotting the data points on a scatter plot,we have observed an inverse relationship between the independent variable (x)and the dependent variable (y).Therefore,we can expect both the sample _ and the sample _________ to be negative values.