Deck 13: Simple Linear Regression Analysis

Question 1

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

Answer 1

False

Question 2

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).

Answer 2

False

Question 3

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

Answer 3

False

Question 4

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 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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 10

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

Question 11

When using simple regression analysis,if there is a strong correlation between the independent and dependent variables,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 12

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

Question 13

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 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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 19

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

When the assumption of __________ residuals (error terms)is violated,the Durbin-Watson statistic is used to test to determine if there is significant _____________ among the residuals.

A)Normality,probability
B)Independent,probability
C)Independent,autocorrelation
D)Normality,autocorrelation

Question 22

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 23

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

A)SSE
B)b₀
C)MSE
D)b₁

Question 24

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 25

If the Durbin-Watson statistic is less than d_L,then we conclude that:

A)There is significant positive autocorrelation.
B)There is significant negative autocorrelation.
C)There is significant autocorrelation,but we cannot identify whether it is positive or negative.
D)The test results are inconclusive.

Question 26

For the same value of 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)The same as
D)Sometimes larger than,sometimes smaller than

Question 27

If the Durbin-Watson statistic is greater than (4 - d_L),then we conclude that:

A)There is significant positive autocorrelation.
B)There is significant negative autocorrelation.
C)There is significant autocorrelation,but we cannot identify whether it is positive or negative.
D)The test result is inconclusive.

Question 28

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

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

Question 29

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

A)Always
B)Sometimes
C)Never

Question 30

If successive values of the residuals are close together,then there is a ___________ autocorrelation,and the value of the Durbin-Watson statistic is _________.

A)Negative,large
B)Positive,small
C)Negative,small
D)Positive,large

Question 31

The ___________ ther²,and the __________ thes (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 32

The Durbin-Watson test statistic ranges from:

A)-4 to 4
B)0 to 4
C)0 to 3
D)-1 to 1
E)0 to 1

Question 33

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 34

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 35

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

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

Question 36

What value of the Durbin-Watson statistic indicates that there is no autocorrelation present in time-ordered data?

A)1
B)-1
C)2
D)-2
E)0

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)A histogram of the residuals forms 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

The 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 39

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 40

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 41

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)a one-unit increase

Question 42

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 43

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 44

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

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

Question 45

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 46

The simple linear regression (least squares method)minimizes:

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

Question 47

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

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

Question 48

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

A)Normality
B)Independence of error terms
C)μ = 0
D)Constant variation

Question 49

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 have either a positive or a negative value.

Question 50

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

A)Always
B)Never
C)Sometimes

Question 51

The following results were obtained as part of a simple regression analysis: 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 52

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

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

Question 53

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 54

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 the coefficient of correlation and the coefficient of determination.

Question 55

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 56

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 57

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 these

Question 58

For a given data set,specific value of X,and 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 59

After plotting the data points 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 60

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 61

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. Determine the standard error.

Question 62

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

Question 63

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 64

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

A)t
B)z
C)r
D)r²

Question 65

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. Calculate the correlation coefficient.

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. Determine SSE and SS(Total).

Question 67

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

Question 68

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

Question 69

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 70

An experiment was performed on a certain metal to determine if the strength is a function of heating time.The simple linear regression equation is The time is in minutes and the strength is measured in pounds per square inch.The 95 percent confidence interval for the slope is from .564 to 1.436.Can we reject β₁ = 0?

Question 71

An experiment was performed on a certain metal to determine if the strength is a function of heating time.The sample size consists of 10 metal sheets.The simple linear regression equation is The time is in minutes and the strength is measured in pounds per square inch.One of the 10 metal sheets was heated for 4 minutes and the resulting strength was 6 lbs.per square inch.Calculate the value of the residual for this observation.

Question 72

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. Using the simple linear regression model,find the estimated y-intercept.

Question 73

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. Using the simple linear regression model,find the estimated y-intercept and slope and write the equation of the least squares regression line.

Question 74

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. Calculate the coefficient of determination.

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. Determine the value of the F statistic.

Question 76

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 The time is in minutes,the strength is measured in pounds per square inch,MSE = 0.5, Determine the 95 percent confidence interval for the mean value of metal strength when the average heating time is 4 minutes.

Question 77

Use the following results obtained from a simple linear regression analysis with 12 observations. Test to determine if there is a significant negative relationship between the independent and dependent variables at α = .05.Give the test statistic and the resulting conclusion.

Question 78

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 79

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. Find the t statistic and test H₀: b₁ ≤ 0 vs.H_a: b₁> 0 at α = .05.

Question 80

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. Calculate the 95 percent confidence interval for the slope.