Deck 11: Correlation Coefficient and Simple Linear Regression Analysis

Question 1

The experimental region is the range of the previously observed values of the dependent variable.

Answer 1

False

Question 2

In a simple linear regression model,the coefficient of determination indicates the strength and direction of the relationship between independent and dependent variable.

Answer 2

False

Question 3

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).

Answer 3

False

Question 4

In simple regression analysis,the quantity $\sum ( y - \bar { y } ) ^ { 2 }$
is called the total variation.

Question 5

The slope in the simple linear regression model represents the average change in the value of the dependent variable per unit change in the independent variable.

Question 6

The dependent variable is the variable that is being described,predicted,or controlled.

Question 7

The least squares simple linear regression line minimizes the sum of the vertical deviations between the line and the data points.

Question 8

A significant positive correlation between x and y implies that changes in x causes y to change.

Question 9

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

Question 10

The residual is the difference between the observed value of the dependent variable and the predicted value of the dependent variable.

Question 11

The standard error of the estimate (standard error)is the estimated standard deviation of the distribution of the independent variable x for all values of the dependent variable y.

Question 12

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.

Question 13

When there is positive autocorrelation,over time,negative error terms are followed by positive error terms and positive error terms are followed by negative error terms.

Question 14

The coefficient of determination is the proportion of total variation explained by the regression line.

Question 15

For simple linear regression model,the least-squares line is the equation that minimizes the sum of the squared deviations between each observed value of y and the line.

Question 16

When using simple regression analysis,if there is a strong positive correlation between the independent and dependent variable,then we can conclude that an increase in the value of the independent variable causes an increase in the value of the dependent variable.

Question 17

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

Question 18

In simple regression analysis,r²measures the proportion of the variation in the dependent variable explained by the simple linear regression model.

Question 19

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

Question 20

A simple linear regression model is an equation that describes the straight-line relationship between a dependent variable and an independent variable.

Question 21

In simple regression analysis,the standard error is ___________ greater than the standard deviation of y values.

A)always
B)sometimes
C)never
D)Cannot be determined.

Question 22

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

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 23

The sample correlation coefficient may assume any value between:

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

Question 24

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.

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

Question 25

When using simple linear regression,we would like to use confidence intervals for the _____ and prediction intervals for the _____ at a given value of x.

A)individual y-value,mean y-value
B)mean y-value,individual y-value
C)slope,mean slope
D)y-intercept,mean y-intercept
E)mean x-value,mean slope

Question 26

The point estimate of the error variance in a regression model is:

A)SSE
B)b₀
C)MSE
D)b₁
E)r

Question 27

The following results were obtained from a simple regression analysis: $$\hat { y }$$ = 37.2895 - 1.2024x, r2 = 0.6744, $$s _ { b _ { 1 } }$$ = 0.2934

-For each unit change in x,the estimated change in the mean of y is equal to:

A)36.0871
B)0.6774
C)37.2895
D)0.2934
E)-1.2024

Question 28

The _____ measures the strength and direction of the linear relationship between the dependent and the independent variable.

A)sample correlation coefficient
B)distance value
C)y Intercept
D)residual
E)coefficient of determination

Question 29

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

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 30

For the same value of x (independent variable),the width of the confidence interval for the average value of y (dependent variable)is ______________ the width of the prediction interval for the individual value of y.

A)greater than
B)less than
C)equal to
D)Cannot be determined without sample data.

Question 31

In a simple linear regression analysis,the sample correlation coefficient r and the estimate of the slope b₁_____ have the same sign.

A)always
B)sometimes
C)never

Question 32

In simple regression analysis,the quantity $\sum ( y - \bar { y } ) ^ { 2 }$
Is called the __________ variation.

A)explained
B)total
C)unexplained
D)block
E)error

Question 33

In simple regression analysis,the quantity $\sum ( y - \bar { y } ) ^ { 2 }$
Is called the __________ variation.

A)explained
B)total
C)unexplained
D)block
E)error

Question 34

Which of the following is a violation of one of the major assumptions of the simple regression model?

A)The error terms are independent of each other.
B)Histogram of the residuals form a bell-shaped,symmetrical curve.
C)The error terms occur in a random pattern over time.
D)As the value of x increases,the value of the error term also increases.
E)The error terms have a mean of zero for any value of x.

Question 35

In performing an F test for a simple linear regression analysis based on 20 observations,the critical F value would have ________ numerator degrees of freedom and _________ denominator degrees of freedom.

A)1,20
B)18,19
C)19,20
D)1,18
E)18,20

Question 36

The following results were obtained from a simple regression analysis: $$\hat { y }$$ = 37.2895 - 1.2024x, r2 = 0.6744, $$s _ { b _ { 1 } }$$ = 0.2934

-When x is equal to zero,the estimated value of the mean of y is equal to:

A)-1.2024
B)6774
C)37.2895
D)2934
E)36.0871

Question 37

The following results were obtained as a part of simple linear regression analysis:
R²= 0.9162
F test statistic = 81.87
At $\alpha$
= 0)05,the null hypothesis of no linear relationship between the dependent variable and the independent variable _____.

A)is rejected.
B)cannot be tested with the given information.
C)is not rejected.

Question 38

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

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

Question 39

In a fitted simple linear regression model,the quantity that estimates the amount by which the mean of Y (dependent variable)changes for a unit change in X (independent variable)is called the _____.

A)coefficient of determination
B)slope of the regression line
C)y intercept of the regression line
D)correlation coefficient
E)standard error

Question 40

In a simple linear regression analysis,if the correlation coefficient is positive,then:

A)The y intercept must also be a positive value.
B)The coefficient of determination can be either positive or negative,depending on the value of the slope.
C)The least squares regression equation could either have a positive or a negative slope.
D)The slope of the regression line must also be positive.
E)The standard error of estimate can either have a positive or a negative value.

Question 41

The strength of the relationship between two quantitative variables can be measured by:

A)The slope of a simple linear regression equation
B)The Y intercept of the simple linear regression equation
C)The sample correlation coefficient
D)The coefficient of determination
E)Both the sample correlation coefficient and the coefficient of determination.

Question 42

For the same set of observations on a specified dependent variable y,two different independent variables x₁and x₂were used to fit two separate simple linear regression models.Model 1 used x₁as the independent variable,and Model 2 used x₂as the independent variable.If the r² values from Model 1 and Model 2 were 0.92 and 0.85,respectively,then we can conclude that:

A)Model 1 has greater utility in predicting y than Model 2.
B)Model 2 has greater utility in predicting y than Model 1.
C)There is not sufficient information to determine which of the two models has greater utility in predicting y.

Question 43

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 population slope for significance at a significance level of .05,what is the rejection point condition for the two-sided t test?

A)Reject H₀if |t| > 2.571
B)Reject H₀if t > 2.571
C)Reject H₀if |t| < 2.571
D)Reject H₀if |t| > 2.051
E)Reject H₀if t > 2.051

Question 44

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.

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

Question 45

Which one of the following statements about the sample correlation coefficient is true?

A)It is always a value between 0 and 1.
B)The represents the proportion of observed variation in the dependent variable that is explained by the fitted regression model.
C)It is measured in the same units as the dependent variable.
D)It is measured in the same units as the independent variable.
E)It is a unitless measurement.

Question 46

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-What is the least-square prediction equation?

A) $\hat { y }$ = 7.9682 + 1.667 x
B) $\hat { y }$ = 63.333 + 6.667 x
C) $\hat { y }$ = 7.948 + 4.000 x
D) $\hat { y }$ = 11.547 + 1.667 x
E) $\hat { y }$ = 6.667 + 63.333 x

Question 47

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-What is the value of the coefficient of determination?

A)11.547
B)762
C)873
D)6.6667
E)1.6667

Question 48

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-Determine a 95% confidence interval estimate of the daily average store sales based on $3000 advertising expenditures? The distance value for this particular prediction is reported as .164.

A)$64,496 to $102.170
B)$33,108 to $133,558
C)$71,312 to $95,356
D)$51,314 to $115,353
E)$42,851 to $83,816

Question 49

The least-squares regression line is the line that minimizes:

A)the explained variation
B)SSyy
C)total variation
D)SSxx
E)SSE

Question 50

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-If the manager decides to spend $3000 on advertising,based on the simple linear regression results given above,the estimated average,or predicted,sales is:

A)$68,333
B)$20,063.33
C)$83,334
D)$20,064,333
E)$70,000

Question 51

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?

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

Question 52

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 SSE?

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

Question 53

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?

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

Question 54

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-What are the limits of the 99% prediction interval of the daily sales in dollars of an individual grocery store that has spent $3000 on advertising expenditures? The distance value for this particular prediction is reported as .164.

A)$64,496 to $102.170
B)$33,104 to $133,564
C)$71,324 to $95,342
D)$51,314 to $115,353
E)$42,851 to $83,816

Question 55

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.

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 56

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?

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 57

In a simple linear regression analysis,when the constant variance assumption for the error term holds,a plot of the residual versus x:

A)Fans out
B)Funnels in
C)Fans out,but then funnels in
D)Forms a horizontal band pattern
E)Suggests an increasing error variance

Question 58

For a given data set,specific value of x,and a confidence level,if all the other factors are constant,the confidence interval for the mean value of y will _______ be wider than the corresponding prediction interval for the individual value of y.

A)always
B)sometimes
C)never
D)Cannot be determined without sample information.

Question 59

An experiment was performed on a certain metal to determine if the strength,in g/cm²,was a function of heating time,in minutes.The least-squares regression line was found to be $\hat { y }$
= 1 + 1x.What is the predicted value strength when the metal is heated for 4 minutes?

A)1 g/cm²
B)2 g/cm²
C)3 g/cm²
D)4 g/cm²
E)5 g/cm²

Question 60

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 }$
$\begin{array}{rrrrrrrr}\hline\text { Variables} & \text { Coefficients } & \text { std. error } & t(d f=5) & \text { p-value } & 95 \% &95 \% \text { upper } \\& & & & & \text { lower } & \\\hline \text { Intercep } & 63.3333 & 7.9682 & 7.948 & .0005 & 42.8505 & 83.8162 \\\text { Advertising } & 6.6667 & 1.6667 & 4.000 & .0103 & &\end{array}$

-What are the limits of the 95% confidence interval for the population slope?

A)5.00 to 8.333
B)2.667 to 10.667
C)4.096 to 9.238
D)2.382 to 10.952
E)3.308 to 10.025

Question 61

The ______ is the range of the previously observed values of the dependent variable.

Question 62

The coefficient of determination measures the proportion of observed variation in the _______ explained by the simple linear regression model.

Question 63

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

-You wish to perform a simple linear regression analysis using x as the independent variable and y as the dependent variable.What is the standard error?

A)212
B)189
C)106
D)460
E)590

Question 64

In simple linear regression,the __________ assumption requires that all variation around the regression line should be equal at all possible values (levels)of the independent variable.

Question 65

The simple linear regression model assumes there is a _____ relationship between the dependent variable and the independent variable.

Question 66

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?

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

Question 67

_____ is a statistical technique in which we use observed data to relate a dependent variable to one or more predictor (independent)variables.

Question 68

While the range for r² is between 0 and 1,the range for r is between ____ and ____.

Question 69

Consider the following partial computer output from a simple linear regression analysis.
$$\begin{array} { l c l c c } \text { Variable } & \text { Coefficient } & \text { Std. Deviation } & \mathrm { T } & \mathrm { P } \\\text { Intercept } & - 28.13 & & - .088 & .9309 \\\mathrm { X } & 1.12 & .04891 & 22.895 & .0001 \\\mathrm { R } ^ { 2 } .9722 & & & &\end{array}$$

-What is the estimated slope?

A)-.088
B)931
C)1.12
D)-28.13
E)9722

Question 70

In a simple linear regression model,the y-intercept term is the mean value of y when x equals _____.

Question 71

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

Question 72

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?

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

Question 73

Consider the following partial computer output from a simple linear regression analysis.
$$\begin{array} { l c l c c } \text { Variable } & \text { Coefficient } & \text { Std. Deviation } & \mathrm { T } & \mathrm { P } \\\text { Intercept } & - 28.13 & & - .088 & .9309 \\\mathrm { X } & 1.12 & .04891 & 22.895 & .0001 \\\mathrm { R } ^ { 2 } .9722 & & & &\end{array}$$

-What is the estimated y-intercept?

A)-.088
B)931
C)22.895
D)-28.13
E)9722

Question 74

Consider the following partial computer output from a simple linear regression analysis.
$$\begin{array} { l c l c c } \text { Variable } & \text { Coefficient } & \text { Std. Deviation } & \mathrm { T } & \mathrm { P } \\\text { Intercept } & - 28.13 & & - .088 & .9309 \\\mathrm { X } & 1.12 & .04891 & 22.895 & .0001 \\\mathrm { R } ^ { 2 } .9722 & & & &\end{array}$$

-What is the correlation coefficient?

A)986
B)972
C)995
D)931
E)948

Question 75

Consider the following partial computer output from a simple linear regression analysis.
$$\begin{array} { l c l c c } \text { Variable } & \text { Coefficient } & \text { Std. Deviation } & \mathrm { T } & \mathrm { P } \\\text { Intercept } & - 28.13 & & - .088 & .9309 \\\mathrm { X } & 1.12 & .04891 & 22.895 & .0001 \\\mathrm { R } ^ { 2 } .9722 & & & &\end{array}$$

-What is the predicted value of y when x = 1,000?

A)2813
B)1120
C)2289
D)1092
E)1000

Question 76

In a simple linear regression model,the slope term is the change in the mean value of y associated with a _____ unit increase in x.

Question 77

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 regression sum of squares,or the explained variation?

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

Question 78

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 degrees of freedom value associated with the error sum of squares,or unexplained variation?

A)1
B)2
C)3
D)4
E)5

Question 79

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 SSxx?

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

Question 80

Any value of the error term in a regression model must be _____ of any other value of the error term.