Question 1

In the simple linear regression model, the slope represents:

Accepted Answer

A)  the value of y when x = 0 
B)  the average change in y per unit change in x 
C)  the value of x when y = 0 
D)  the average change in x per unit change in y 
E)  all of these 
A)  the value of y when x = 0 
B)  the average change in y per unit change in x 
C)  the value of x when y = 0 
D)  the average change in x per unit change in y 
E)  all of these

Question 2

The value of the sum of squares for regression SSR can never be larger than the value of sum of squares for error SSE.

Accepted Answer

A) True 
 B)False

Question 3

An automobile company in Michigan is interested in the relationship between the gender of their employees and employee productivity. A good starting point in this analysis would be to compute the coefficient of determination and the correlation coefficient.

Accepted Answer

A) True 
 B)False

Question 4

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line:   = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

Accepted Answer

A) True 
 B)False

Question 5

In a simple linear regression model, if the regression model is statistically significant, then the regression slope coefficient is significantly greater than zero.

Accepted Answer

A) True 
 B)False

Question 6

The sum of squares for regression (SSR) can never be larger than the sum of squares for error (SSE).

Accepted Answer

A) True 
 B)False

Question 7

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

Accepted Answer

A)  1.350 
B)  1.771 
C)  2.160 
D)  2.650 
E)  2.260 
A)  1.350 
B)  1.771 
C)  2.160 
D)  2.650 
E)  2.260

Question 8

In a simple linear regression problem, the least squares line is   = 2.73 - 1.02x, and the coefficient of determination is 0.7744. The correlation coefficient must be -0.88.

Accepted Answer

A) True 
 B)False

Question 9

Let x be the area (in square feet) to be covered with blacktop and let y be the time (in minutes) it takes a construction crew to completely cover the area. The simple linear regression model relates x and y where the least squares estimates of the regression parameters are b = 0.207 and a = 81.6.
What is the least-squares best-fitting regression line?   = ______________
What is the estimated amount of time it takes to apply 2400 square feet of blacktop?
______________ (minutes)
What is the average change in time per one square foot increase in area?
______________ (minutes)

Accepted Answer

81.6 + 0.2

Question 10

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line:   = 120 + 5x. This implies that if the height is increased by 1 inch, the weight, on average, is expected to:

Accepted Answer

A)  increase by 1 pound 
B)  decrease by 1 pound 
C)  increase by 5 pounds 
D)  increase by 24 pounds 
E)  increase by 125 pounds 
A)  increase by 1 pound 
B)  decrease by 1 pound 
C)  increase by 5 pounds 
D)  increase by 24 pounds 
E)  increase by 125 pounds

Question 11

In developing 90% prediction interval for the particular value of y from a simple linear regression problem involving a sample of size 14, the appropriate table value would be 2.179.

Accepted Answer

A) True 
 B)False

Question 12

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -.85.

Accepted Answer

A) True 
 B)False

Question 13

A professor of economics wants to study the relationship between income (y in $1000s) and education (x in years). A random sample eight individuals is taken and the results are shown below.   Predict with 95% confidence the income of an individual with 10 years of education.
CI = ______________ Enter (n1, n2) in thousands
Estimate with 95% confidence the average income of all individuals with 10 years of education.
CI = ______________ Enter (n1, n2) in thousands
Which interval in the previous two questions is narrower: the confidence interval estimate of the expected value of y or the prediction interval for the same given value of x (10 years) and same confidence level?
______________
Why?
________________________________________________________

Accepted Answer

(37.005, 42.425); (38.527, 40.

Question 14

In a simple linear regression problem, suppose the sum of squares for regression (SSR) is 90. Which of the following must be true?

Accepted Answer

A)  The correlation coefficient is 0.9. 
B)  The coefficient of determination is 0.81. 
C)  The total sum of squares (Total SS) is at least 90. 
D)  The sum of squares for error (SS
E)  is at most 90. 
E)  The coefficient of determination is 90. 
A)  The correlation coefficient is 0.9. 
B)  The coefficient of determination is 0.81. 
C)  The total sum of squares (Total SS) is at least 90. 
D)  The sum of squares for error (SS
E)  is at most 90. 
E)  The coefficient of determination is 90.

Question 15

A medical statistician wanted to examine the relationship between the amount of sunshine (x) in hours, and incidence of skin cancer (y). As an experiment he found the number of skin cancers detected per 100,000 of population and the average daily sunshine in eight counties around the country. These data are shown below.   Determine the least squares regression line.   = ______________
Draw a scatter diagram of the data and plot the least squares regression line on it.
Estimate the number of skin cancer per 100,000 of population for 6 hours of sunshine.
______________
Calculate the residual corresponding to the pair (x, y) = (8, 15).
______________

Accepted Answer

-1.115 + 1

Question 16

In regression analysis, the residuals represent the:

Accepted Answer

A)  difference between the actual y values and their predicted values 
B)  difference between the actual x values and their predicted values 
C)  square root of the slope of the regression line 
D)  change in y per unit change in x 
E)  difference between the actual x and y values 
A)  difference between the actual y values and their predicted values 
B)  difference between the actual x values and their predicted values 
C)  square root of the slope of the regression line 
D)  change in y per unit change in x 
E)  difference between the actual x and y values

Question 17

If the plot of the residuals is fan shaped, which assumption of regression analysis if violated?

Accepted Answer

A)  Normality. 
B)  Homoscedasticity. 
C)  Independence of errors. 
D)  No assumptions are violated, the graph should resemble a fan. 
E)  All of these. 
A)  Normality. 
B)  Homoscedasticity. 
C)  Independence of errors. 
D)  No assumptions are violated, the graph should resemble a fan. 
E)  All of these.

Question 18

In a simple linear regression analysis, it was stated that the correlation between starting salary and years of experience is 0.80. This indicates that 80% of the variation in starting salary is explained by years of experience.

Accepted Answer

A) True 
 B)False

Question 19

A study was conduced to determine the effect of extra help sessions attended on students ability to avoid mistakes on a 20- multiple choice test. The data shown below represent the number of extra help sessions attended (x) and the average number of mistakes (y) recorded.   Use the regression formulas to find the least-squares line for the data.   = ______________
Plot the six points and graph the line.
Does the line appear to provide a good fit to the data points?
______________
Use the least-Squares line to predict the value of y when x = 3.5.
______________
Do the data provide sufficient evidence to indicate that y and x are linearly related at the 1% level of significance?
p-value:
______________
Conclude:
______________
y and x ______________ linearly related.
Calculate the coefficient of determination.
r2 = ______________
What information does this value give about the usefulness of the linear model?
________________________________________________________

Accepted Answer

-0.55714x + 6.5; @#IMG-DLM& ;
Yes; 4.55; .000248;

Question 20

Given the least squares regression line   = -2.48 + 1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Accepted Answer

A)  -0.85 
B)  0.85 
C)  -0.90 
D)  0.90 
E)  -0.81 
A)  -0.85 
B)  0.85 
C)  -0.90 
D)  0.90 
E)  -0.81

In the simple linear regression model, the slope represents:

The value of the sum of squares for regression SSR can never be larger than the value of sum of squares for error SSE.

An automobile company in Michigan is interested in the relationship between the gender of their employees and employee productivity. A good starting point in this analysis would be to compute the coefficient of determination and the correlation coefficient.

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

In a simple linear regression model, if the regression model is statistically significant, then the regression slope coefficient is significantly greater than zero.

The sum of squares for regression (SSR) can never be larger than the sum of squares for error (SSE).

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

In a simple linear regression problem, the least squares line is = 2.73 - 1.02x, and the coefficient of determination is 0.7744. The correlation coefficient must be -0.88.

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: = 120 + 5x. This implies that if the height is increased by 1 inch, the weight, on average, is expected to:

In developing 90% prediction interval for the particular value of y from a simple linear regression problem involving a sample of size 14, the appropriate table value would be 2.179.

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -.85.

In a simple linear regression problem, suppose the sum of squares for regression (SSR) is 90. Which of the following must be true?

In regression analysis, the residuals represent the:

If the plot of the residuals is fan shaped, which assumption of regression analysis if violated?

In a simple linear regression analysis, it was stated that the correlation between starting salary and years of experience is 0.80. This indicates that 80% of the variation in starting salary is explained by years of experience.

Given the least squares regression line = -2.48 + 1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters

Exam 12: Linear Regression and Correlation

In the simple linear regression model, the slope represents:

The value of the sum of squares for regression SSR can never be larger than the value of sum of squares for error SSE.

An automobile company in Michigan is interested in the relationship between the gender of their employees and employee productivity. A good starting point in this analysis would be to compute the coefficient of determination and the correlation coefficient.

A regression analysis between sales (in $1000) and advertising (in $100) resulted in the following least squares line: = 77 +8x. This implies that if advertising is $600, then the predicted amount of sales (in dollars) is $125,000.

In a simple linear regression model, if the regression model is statistically significant, then the regression slope coefficient is significantly greater than zero.

The sum of squares for regression (SSR) can never be larger than the sum of squares for error (SSE).

In order to predict with 80% confidence the expected value of y for a given value of x in a simple linear regression problem, a random sample of 15 observations is taken. Which of the following t-table values listed below would be used?

In a simple linear regression problem, the least squares line is = 2.73 - 1.02x, and the coefficient of determination is 0.7744. The correlation coefficient must be -0.88.

A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: = 120 + 5x. This implies that if the height is increased by 1 inch, the weight, on average, is expected to:

In developing 90% prediction interval for the particular value of y from a simple linear regression problem involving a sample of size 14, the appropriate table value would be 2.179.

In simple linear regression analysis, if the correlation coefficient between the independent variable x and the dependent variable y is -.85, this means that the scatterplot generated by the same data values would show points that would fall on a straight line with slope equal to -.85.

In a simple linear regression problem, suppose the sum of squares for regression (SSR) is 90. Which of the following must be true?

In regression analysis, the residuals represent the:

If the plot of the residuals is fan shaped, which assumption of regression analysis if violated?

In a simple linear regression analysis, it was stated that the correlation between starting salary and years of experience is 0.80. This indicates that 80% of the variation in starting salary is explained by years of experience.

Given the least squares regression line = -2.48 + 1.63x, and a coefficient of determination of 0.81, the coefficient of correlation is:

Describing Data With Graphs

Describing Data With Numerical Measures

Describing Bivariate Data

Probability and Probability Distributions

Several Useful Discrete Distributions

The Normal Probability Distribution

Sampling Distributions

Large-Sample Estimation

Large-Sample Tests of Hypotheses

Inference From Small Samples

The Analysis of Variance

Multiple Regression Analysis

Analysis of Categorical Data

Nonparametric Statistics

Filters