Deck 13: Simple Linear Regression Analysis

Question 1

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.

Answer 1

False

Question 2

If r = -1,then we can conclude that there is a perfect relationship between X and Y.

Answer 2

True

Question 3

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).

Answer 3

False

Question 4

The estimated simple linear regression equation minimizes the sum of the squared deviations between each value of Y and the line.

Question 5

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

Question 6

The slope of the simple linear regression equation represents the average change in the value of the dependent variable per unit change in the independent variable (X).

Question 7

The notation refers to the average value of the dependent variable Y.

Question 8

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

Question 9

In simple linear regression analysis,if the error terms exhibit a positive or negative autocorrelation over time,then the assumption of constant variance is violated.

Question 10

When using simple regression analysis,if there is a strong 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 11

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

Question 12

In a simple linear regression model,the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable,but also shows whether the relationship is positive or negative.

Question 13

The error term is the difference between an individual value of the dependent variable and the corresponding mean value of the dependent variable.

Question 14

In simple regression analysis,r² is a percentage measure and measures the proportion of the variation explained by the simple linear regression model.

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

A significant positive correlation between X and Y implies that changes in X cause Y to change.

Question 21

The following results were obtained as a part of simple regression analysis: r²= .9162
F statistic from the F table = 3.59
Calculated value of F from the ANOVA table = 81.87 = .05
P-value = .000
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
D)is not an appropriate null hypothesis for this situation

Question 22

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

A)Always
B)Sometimes
C)Never

Question 23

The correlation coefficient may assume any value between

A)0 and 1
B)- $\infty$ and $\infty$
C)0 and 8
D)-1,and 1
E)-1,and 0

Question 24

For the same value X (independent variable),the confidence interval for the average value of Y (dependent variable)is __________________ the prediction interval for the individual value of Y.

A)Larger than
B)Smaller than
C)Same as
D)Sometimes larger than sometimes smaller than

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

Question 26

In a simple regression analysis for a given data set,if the null hypothesis $\beta$ = 0 is rejected,then the null hypothesis $\rho$ = 0 is also rejected.This statement is ___________ true.

A)Always
B)Never
C)Sometimes

Question 27

The following results were obtained from a simple regression analysis: = 37.2895 - (1.2024)X r²= .6744 s_b = .2934
When X (independent variable)is equal to zero,the estimated value of Y (dependent variable)is equal to:

A)-1.2024
B).6774
C)37.2895
D).2934

Question 28

The following results were obtained from a simple regression analysis: = 37.2895 - (1.2024)X r²= .6744 s_b = .2934
____________ is the proportion of the variation explained by the simple linear regression model.

A)-1.2024
B).6774
C)37.2895
D).2934

Question 29

The point estimate of the variance in a regression model is

A)SSE
B)b₀
C)MSE
D)b₁

Question 30

In a simple linear regression analysis,the correlation coefficient (a)and the slope (b)_____ have the same sign.

A)always
B)sometimes
C)never

Question 31

In simple regression analysis,if the correlation coefficient is a positive value,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 32

The ___________ the r²,and the __________ the s (standard error),the stronger the relationship between the dependent variable and the independent variable.

A)Higher,lower
B)Lower,higher
C)Lower,lower
D)Higher,higher

Question 33

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

A)Correlation coefficient
B)Distance value
C)Y Intercept
D)Residual

Question 34

In simple regression analysis the quantity that gives the amount by which 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 35

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 are dependent on each other.

Question 36

A simple regression analysis with 20 observations would yield ________ degrees of freedom error and _________ degrees of freedom total.

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

Question 37

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 show no pattern.
D)As the value of x increases,the value of the error term also increases.

Question 38

In simple regression analysis,the quantity is called the __________ sum of squares.

A)Total
B)Explained
C)Unexplained
D)Error
E)Standard Error

Question 39

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 40

The following results were obtained from a simple regression analysis: = 37.2895 - (1.2024)X r²= .6744 s_b = .2934
For each unit change in X (independent variable),the estimated change in Y (dependent variable)is equal to:

A)-1.2024
B).6774
C)37.2895
D).2934

Question 41

Regression Analysis The 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.He 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 above summarizes the results of the regression model. 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 42

Regression Analysis The 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.He 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 above summarizes the results of the regression model. In testing the simple linear regression equation for significance at a significance level of .05,what is the rejection point condition?

A)Reject H₀ if F > 16.26
B)Reject H₀ if F > 10.01
C)Reject H₀ if F > 6.61
D)Reject H₀ if F > 230.2
E)Reject H₀ if F > 5.79

Question 43

After plotting the data point s on a scatter diagram,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 44

When the constant variance assumption 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 45

The coefficient of determination measures the ________ explained by the simple linear regression model.

A)Correlation
B)Proportion of variation
C)Standard error
D)Mean square error

Question 46

Which of the following is a violation of the independence assumption?

A)Negative autocorrelation
B)A pattern of cyclical error terms over time
C)Positive autocorrelation
D)A pattern of alternating error terms over time
E)All of the above

Question 47

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

A)normality
B)control variation
C)constant variance
D)independence

Question 48

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 coefficient of correlation
D)The coefficient of determination
E)Both C and D above

Question 49

Regression Analysis The 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.He 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 above summarizes the results of the regression model. If the manager decides to spend $3000 on advertising,based on the simple linear regression results given above,the estimated sales are:

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

Question 50

The _____ of the simple linear regression model is the value of y when the mean value of x is zero.

A)y-intercept
B)slope
C)independent variable
D)response variable

Question 51

Regression Analysis The 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.He 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 above summarizes the results of the regression model. At a significance level of .05,test the significance of the slope and state your conclusion.

A)We reject H₀ and conclude there is sufficient evidence that dollars spent on advertising is a useful linear predictor of the grocery store sales.
B)We failed to reject H₀ and conclude there is not sufficient evidence that dollars spent on advertising is a useful linear predictor of the grocery store sales.
C)We failed to reject H₀ and conclude there is sufficient evidence that dollars spent on advertising is a useful linear predictor of the grocery store sales.
D)We reject H₀ and conclude that there is sufficient evidence that grocery store sales in dollars is a useful linear predictor of the dollars spent on advertising.
E)We reject H₀ and conclude that there is not sufficient evidence that dollars spent on advertising is a useful linear predictor of the grocery store sales.

Question 52

The simple linear regression (least squares method)minimizes:

A)The explained variation
B)SS_yy
C)Total variation
D)SS_xx
E)SSE

Question 53

Regression Analysis The 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.He 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 above summarizes the results of the regression model. 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)$71,324 to $95,342
D)$51,314 to $115,353
E)$42,851 to $83,816

Question 54

Regression Analysis The 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.He 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 above summarizes the results of the regression model. What is the value of the simple coefficient of determination?

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

Question 55

Regression Analysis The 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.He 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 above summarizes the results of the regression model. 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)$33,108 to $133,558
C)$71,324 to $95,342
D)$51,314 to $115,353
E)$42,851 to $83,816

Question 56

Regression Analysis The 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.He 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 above summarizes the results of the regression model. In testing the population for significance at a significance level of .05,what is the rejection point condition for the two-sided test?

A)Reject H₀ if |t| > 2.571
B)Reject H₀ if t > 2.571
C)Reject H₀ if |t| < 2.571
D)Reject H₀ if |t| > 2.051
E)Reject H₀ if t > 2.051

Question 57

For the same set of observations on a specified dependent variable two different independent variables were used to develop two separate simple linear regression models.A portion of the results is presented below. Based on the results given above,we can conclude that:

A)A prediction based on Model 1 is better than a prediction based on Model 2.
B)A prediction based on Model 2 is better than a prediction based on Model 1.
C)There is no difference in the predictive ability between Model 1 and Model 2.
D)There is not sufficient information to determine which of the two models is superior for prediction purposes.

Question 58

Regression Analysis The 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.He 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 above summarizes the results of the regression model. What is the estimated simple linear regression equation?

A)
B)
C)
D)
E)

Question 59

The range for r² is between 0 and 1 and the range for r is between ________

A)0 and 1
B)-1 and 1
C)-1 and 0
D)no limit

Question 60

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

Question 61

A _______________ is a method or a process of estimating a relationship between a dependent variable (Y)and a single independent variable (X).

A)Chi-square analysis
B)Simple linear regression analysis
C)One-way ANOVA
D)Correlation analysis

Question 62

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. = 30 = 104 = 40 = 178 = 134 Determine SSE,SS (Total)

A)10,14
B)4,18
C)14,18
D)17,18

Question 63

If the points are tightly distributed around the regression line on a scatter diagram,then we can conclude that the changes in the value of the dependent variable _________ the independent variable (X).

A)have no relationship with
B)are explained by
C)always inversely related to
D)always positively related to

Question 64

If one of the assumptions of the regression model is violated,performing data transformations on the ____________ can remedy the situation.

A)independent variable
B)slope
C)predictor variable
D)response variable

Question 65

If there is significant autocorrelation present in a data set the ________________ assumption is violated.

A)Normality
B)Independence of error terms
C) $\mu$ = 0
D)Constant variation

Question 66

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. = 30 = 104 = 40 = 178 = 134 Find the estimated y intercept and slope and write the equation of the least squares regression line.

A)14 - 68x
B)2 + 0x
C)0 + 1x
D)1 + 1x

Question 67

The ____________________ is the proportion of the total variation in the dependent variable explained by the regression model.

A)Coefficient of determination
B)Correlation coefficient
C)Slope
D)Standard error

Question 68

A ______________________ measures the strength of the relationship between a dependent variable (Y)and an independent variable (X).

A)Coefficient of determination
B)Correlation coefficient
C)Slope
D)Standard error

Question 69

_____ distribution is used for testing the significance of the slope term.

A)t
B)Z
C)r
D)r²

Question 70

Use the following results obtained from a simple linear regression analysis with 12 observations. = 37.2895 - (1.2024)X r² = .6744 s_b = .2934
Test to determine if there is a significant negative relationship between the independent and dependent variable at $\alpha$ = .05.Give the test statistic and the resulting conclusion.

A)Reject H₀,t = -4.10
B)Fail to reject H₀,t = 4.10
C)Reject H₀,t = -1.783
D)Fail to reject H₀,t = 1.783

Question 71

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. = 30 = 104 = 40 = 178 = 134 Find the estimated y-intercept.

A)1
B)4.45
C)10.04
D)1.289

Question 72

After plotting the data point s on a scatter diagram,we have observed an inverse relationship between the independent variable (X)and the dependent variable (Y).Therefore,we can expect both the sample slope and the __________ to be a negative value.

A)Coefficient of determination
B)Correlation coefficient
C)Slope
D)Standard error

Question 73

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

A)increases with
B)dependent on
C)independent of
D)exactly the same as

Question 74

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

A)Chi-square analysis
B)Regression analysis
C)One-way ANOVA
D)Correlation analysis

Question 75

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. = 30 = 104 = 40 = 178 = 134 Determine the value of the F statistic.

A)28
B)7
C)14
D)12.6

Question 76

The ______ is the range of the previously observed values of x.

A)Population region
B)Experimental region
C)Slope
D)Coefficient of determination

Question 77

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

A)1
B)0
C)-1
D)y

Question 78

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

A)SS Error
B)Total variance
C)MS Error
D)Explained variance

Question 79

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

A)a corresponding increase
B)a variable change
C)no change
D)one unit increase

Question 80

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

A)normal relationship
B)reverse relationship
C)linear relationship
D)correlation