Deck 14: Simple Linear Regression

Question 1

The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the​

A) ​correlation coefficient.
B) ​standard error of the estimate.
C) ​coefficient of determination.
D) ​confidence interval estimate.

Answer 1

​coefficient of determination.

Question 2

In regression analysis, which of the following assumptions is not true about the error term ε?

A) The expected value of the error term is one.
B) The variance of the error term is the same for all values of x.
C) The values of the error term are independent.
D) The error term is normally distributed.

Answer 2

The expected value of the error term is one.

Question 3

The coefficient of correlation

A) is the square of the r-square.
B) is the square root of the r-square.
C) can never be equal to r-square.
D) can never be negative.

Answer 3

is the square root of the r-square.

Question 4

In simple linear regression, r² is the​

A) ​mean square error.
B) ​correlation coefficient.
C) squared residual.
D) ​coefficient of determination.

Question 5

The mathematical equation relating the independent variable to the expected value of the dependent variable; that is, E(y) = β₀ + β₁x, is known as the

A) regression equation.
B) correlation model.
C) estimated regression equation.
D) regression model.

Question 6

The coefficient of determination

A) cannot be negative.
B) is the square root of the coefficient of correlation.
C) is the same as the coefficient of correlation.
D) can be negative or positive.

Question 7

The standard error of the estimate is the

A) standard deviation of t.
B) square root of SSE.
C) square root of SST.
D) square root of MSE.

Question 8

In regression analysis, the unbiased estimate of the variance is

A) coefficient of correlation.
B) coefficient of determination.
C) mean square error.
D) slope of the regression equation.

Question 9

In regression analysis, the model in the form y = $\beta _ { 0 }$ + $\beta _ { 1 }$ x + $\varepsilon$ is called the

A) regression equation.
B) correlation model.
C) estimated regression equation.
D) regression model

Question 10

The model developed from sample data that has the form of $\hat { y }$ = b₀ + b₁x is known as the

A) regression equation.
B) correlation model.
C) estimated regression equation.
D) regression model.

Question 11

If only MSE is known, you can compute the

A) r-square.
B) coefficient of correlation.
C) standard error.
D) ith residual.

Question 12

The interval estimate of the mean value of y for a given value of x is the

A) prediction interval estimate.
B) confidence interval estimate.
C) average regression interval.
D) x versus y correlation interval.

Question 13

The value of the coefficient of correlation (r)

A) can be equal to the value of the coefficient of determination (r²).
B) can never be equal to the value of the coefficient of determination (r²).
C) is always smaller than the value of the coefficient of determination (r²).
D) is always larger than the value of the coefficient of determination (r²).

Question 14

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: $\hat { y }$ = 30,000 + 4x

The above equation implies that an

A) increase of $4 in advertising is associated with an increase of $4000 in sales.
B) increase of $1 in advertising is associated with an increase of $4 in sales.
C) increase of $1 in advertising is associated with an increase of $34,000 in sales.
D) increase of $1 in advertising is associated with an increase of $4000 in sales.

Question 15

In the following estimated regression equation $\hat { y }$ = b₀ + b₁x,

A) b₁ is the slope.
B) b₁ is the intercept.
C) b₁x is the slope.
D) b₁x is the intercept.

Question 16

Regression analysis is a statistical procedure for developing a mathematical equation that describes how

A) one independent and one or more dependent variables are related.
B) several independent and several dependent variables are related.
C) one dependent and one or more independent variables are related.
D) one dependent, one independent, and several error variables are related.

Question 17

If the coefficient of determination is a positive value, then the coefficient of correlation

A) must also be positive.
B) must be zero.
C) can be either positive or negative.
D) can be larger than 1.

Question 18

The interval estimate of an individual value of y for a given value of x is the

A) prediction interval estimate.
B) confidence interval estimate.
C) average regression interval.
D) x versus y correlation interval.

Question 19

In regression analysis, the error term $\varepsilon$ is a random variable with a mean or expected value of

A) 0.
B) 1.
C) $\mu$ .
D) $\bar { x }$ .

Question 20

In a regression analysis, the standard error of the estimate is determined to be 4.In this situation, the MSE

A) is 2.
B) is 16.
C) depends on the sample size.
D) requires a known SSE.

Question 21

Which of the following is correct?

A) SSE= SSR + SST
B) SSR = SSE+SST
C) SST= SSR + SSE
D) SST = SSR - SSE

Question 22

In a simple linear regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then

A) there is a positive correlation between x and y.
B) if x is increased, y must also increase.
C) if y is increased, x must also increase.
D) the estimated regression line intercepts the positive y-axis.

Question 23

If there is a very weak correlation between two variables, then the coefficient of determination must be

A) much larger than 1, if the correlation is positive.
B) much smaller than -1, if the correlation is negative.
C) equal to one.
D) closer or equal to zero.

Question 24

Regression analysis was applied between demand for a product (y) and the price of the product (x), and the following estimated regression equation was obtained. $\hat { y }$ = 120 - 10x

Based on the above estimated regression equation, if price is increased by 2 units, then demand is expected to

A) increase by 120 units.
B) decrease by 100 units.
C) increase by 20 units.
D) decease by 20 units.

Question 25

The equation that describes how the dependent variable (y) is related to the independent variable (x) is called

A) the correlation model.
B) the regression model.
C) correlation analysis.
D) estimation analysis.

Question 26

If the coefficient of determination is equal to 1, then the coefficient of correlation

A) must also be +1.
B) can be either -1 or +1.
C) can be any value between -1 to +1.
D) must be -1.

Question 27

In a regression and correlation analysis, if r² = 1, then

A) SSE must also be equal to one.
B) SSE must be equal to zero.
C) SSE can be any positive value.
D) SSE must be negative.

Question 28

In a regression analysis, the coefficient of correlation is .16.The coefficient of determination in this situation is

A) .4000.
B) .0256.
C) 4.00.
D) 2.56.

Question 29

Larger values of r² imply that the observations are more closely grouped about the

A) average value of the independent variables.
B) average value of the dependent variable.
C) least squares line.
D) origin.

Question 30

If the coefficient of correlation is .8, the percentage of variation in the dependent variable explained by the variation in the independent variable is

A) .80%.
B) 80%.
C) .64%.
D) 64%.

Question 31

Correlation analysis is used to determine

A) the equation of the regression line.
B) the strength of the linear relationship between the dependent and the independent variables.
C) a specific value of the dependent variable for a given value of the independent variable.
D) a cause-and-effect relationship between the dependent and the independent variables.

Question 32

In simple linear regression analysis, which of the following is not true?

A) The F test and the t test yield the same conclusion.
B) The F test and the t test may or may not yield the same conclusion.
C) The relationship between x and y is represented by a straight line.
D) The value of F = t².

Question 33

In regression and correlation analysis, if SSE and SST are known, then with this information the

A) coefficient of determination can be computed.
B) slope of the regression line can be computed.
C) y-intercept can be computed.
D) x-intercept can be computed.

Question 34

In a regression analysis, the coefficient of determination is .4225.The coefficient of correlation in this situation is

A) .65 if b₁ is positive.
B) .1785.
C) -.18 if b₁ is negative.
D) .4225.

Question 35

In a regression and correlation analysis, if r² = 1, then

A) SSE = SST.
B) SSE = 1.
C) SSR = SSE.
D) SSR = SST.

Question 36

In a regression analysis, the regression equation is given by y = 12 - 6x.If SSE = 510 and SST = 1000, then the coefficient of correlation is

A) -.7.
B) +.7.
C) .49.
D) -.49.

Question 37

In regression analysis, if the independent variable is measured in pounds, the dependent variable

A) must also be in pounds.
B) must be in some unit of weight.
C) cannot be in pounds.
D) can be measured in any units.

Question 38

In a regression analysis, if SSE = 200 and SSR = 300, then the coefficient of determination is

A) .67.
B) .60.
C) .40.
D) .20.

Question 39

In regression analysis, the independent variable is

A) used to predict other independent variables.
B) used to predict the dependent variable.
C) the variable that is not used for prediction.
D) the variable that is being predicted.

Question 40

In regression analysis, the variable that is being predicted is the

A) dependent variable.
B) independent variable.
C) intercept variable.
D) error variable.

Question 41

In a regression analysis, if SST = 500 and SSE = 300, then the coefficient of determination is

A) .20.
B) .67.
C) .60.
D) .40.

Question 42

If all the points of a scatter diagram lie on the least squares regression line, then the coefficient of determination for these variables based on these data

A) is 0.
B) is 1.
C) is either 1 or -1, depending upon whether the relationship is positive or negative.
D) could be any value between -1 and 1.

Question 43

If the coefficient of correlation is .90, then the coefficient of determination

A) is also .90.
B) is either .81 or -.81.
C) will be -.90.
D) must be .81.

Question 44

If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the variation in the independent variable is

A) 40%.
B) 16%.
C) 4%.
D) 63%.

Question 45

If there is a very strong correlation between two variables, then the coefficient of determination must be

A) much larger than 1, if the correlation is positive.
B) much smaller than -1, if the correlation is negative.
C) equal to zero.
D) closer or equal to 1.

Question 46

A regression analysis between demand (y in 1000 units) and price (x in dollars) resulted in the following equation: $\hat { y }$ = 9 - 3x

The above equation implies that if the price is increased by $1, the demand is expected to

A) increase by 6 units.
B) decrease by 3 units.
C) decrease by 6000 units.
D) decrease by 3000 units.

Question 47

If the coefficient of correlation is a positive value, then the

A) intercept of the regression line must also be positive.
B) coefficient of determination can be either a negative or a positive value, depending on the slope.
C) regression equation could have either a positive or a negative slope.
D) slope of the regression line must be positive.

Question 48

Compared to the confidence interval estimate for a particular value of y in a linear regression model, the interval estimate for an average value of y will be

A) narrower.
B) wider.
C) the same.
D) easy to determine.

Question 49

If the coefficient of correlation is -.4, then the slope of the regression line

A) must also be -.4.
B) can be either negative or positive.
C) must be negative.
D) must be .16.

Question 50

A least squares regression line

A) can be used to predict a value of y if the corresponding x value is given.
B) implies a cause-and-effect relationship between x and y.
C) can only be determined if a good linear relationship exists between x and y.
D) ensures that the predictions of y outside the range of the values of x are valid.

Question 51

SSE can never be

A) larger than SST.
B) smaller than SST.
C) equal to one.
D) equal to zero.

Question 52

If two variables, x and y, have a strong linear relationship, then

A) there may or may not be any causal relationship between x and y.
B) x causes y to happen.
C) y causes x to happen.
D) the F test is used to conclude there is a causal relationship between x and y.

Question 53

It is possible for the coefficient of determination to be

A) larger than 1.
B) less than 1.
C) less than -1.
D) equal to -1.

Question 54

If a data set produces SSR = 400 and SSE = 100, then the coefficient of determination is

A) .10.
B) .25.
C) .40.
D) .80.

Question 55

In regression analysis, if the dependent variable is measured in dollars, the independent variable

A) must also be in dollars.
B) must be in some units of currency.
C) can be measured in any units.
D) cannot be in dollars.

Question 56

Regression analysis was applied between sales (in $10,000) and advertising (in $100) and the following regression function was obtained. $\hat { y }$ = 50 + 8x

Based on the above estimated regression line, if advertising is $1000, then the point estimate for sales (in dollars) is

A) $8050.
B) $130.
C) $130,000.
D) $1,300,000.

Question 57

If the coefficient of correlation is a negative value, then the coefficient of determination

A) must also be negative.
B) must be zero.
C) can be either negative or positive.
D) will be positive.

Question 58

In a regression analysis, if SST = 4500 and SSE = 1575, then the coefficient of determination is

A) .35.
B) .65.
C) .85.
D) .45.

Question 59

Regression analysis was applied between sales (in $1000) and advertising (in $100) and the following regression function was obtained. $\hat { y }$ = 500 + 4x

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

A) $900.
B) $900,000.
C) $40,500.
D) $505,000.

Question 60

A regression analysis between sales (in $1000) and price (in dollars) resulted in the following equation: $\hat { y }$ = 60 - 8x

The above equation implies that an

A) increase of $1 in price is associated with a decrease of $8 in sales.
B) increase of $8 in price is associated with a decrease of $52,000 in sales.
C) increase of $1 in price is associated with a decrease of $52 in sales.
D) increase of $1 in price is associated with a decrease of $8000 in sales.

Question 61

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. $$\begin{array} { l } \widehat { y } = 12 + 1.8 x \\n = 17 \\\mathrm { SSR } = 225 \\\mathrm { SSE } = 75 \\\mathrm {~s} b _ { 1 } = .2683\end{array}$$
To perform an F test, the p-value is

A) less than .01.
B) between .01 and .025.
C) between .025 and .05.
D) greater than .10.

Question 62

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. $$\hat { y }$$ = 12 + 1.8x

N = 17
SSR = 225
SSE = 75
Sb₁ = .2683
The t statistic for testing the significance of the slope is

A) 1.80.
B) 1.96.
C) 6.71.
D) .56.

Question 63

The following information regarding a dependent variable (y) and an independent variable (x) is provided. $$\begin{array} { l l } y & x \\4 & 2 \\3 & 1 \\4 & 4 \\6 & 3 \\8 & 5\end{array}$$
SSE = 6
SST = 16

The coefficient of determination is

A) .7906.
B) -.7906.
C) .625.
D) .375.

Question 64

If the coefficient of determination is .90, the percentage of variation in the dependent variable explained by the variation in the independent variable is

A) .90%.
B) 90%.
C) 81%.
D) .81%.

Question 65

The following information regarding a dependent variable (y) and an independent variable (x) is provided. $$\begin{array} { l l } y & x \\4 & 2 \\3 & 1 \\4 & 4 \\6 & 3 \\8 & 5\end{array}$$
SSE = 6
SST = 16

The coefficient of correlation is

A) .7906.
B) -.7906.
C) .625.
D) .375.

Question 66

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$$ The least squares estimate of the intercept or b₀ equals

A) 1.
B) -1.
C) 6.
D) -5.

Question 67

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$$
The sample correlation coefficient equals

A) -.4364.
B) .4364.
C) -.1905.
D) .1905.

Question 68

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$$ The sample correlation coefficient equals

A) 0.
B) +1.
C) -1.
D) -.5.

Question 69

The following information regarding a dependent variable (y) and an independent variable (x) is provided. $$\begin{array} { l l } y & x \\4 & 2 \\3 & 1 \\4 & 4 \\6 & 3 \\8 & 5\end{array}$$
SSE = 6
SST = 16

The MSE is

A) 1.
B) 2.
C) 3.
D) 4.

Question 70

The following information regarding a dependent variable (y) and an independent variable (x) is provided. $$\begin{array} { l l } y & x \\4 & 2 \\3 & 1 \\4 & 4 \\6 & 3 \\8 & 5\end{array}$$
SSE = 6
SST = 16

The least squares estimate of the slope is

A) 1.
B) 2.
C) 3.
D) 4.

Question 71

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$$ The least squares estimate of the intercept or b₀ equals

A) 1.
B) -1.
C) -11.
D) 11.

Question 72

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$$ The point estimate of y when x = 2 is

A) -10.
B) 10.
C) -4.
D) 4.

Question 73

The following information regarding a dependent variable (y) and an independent variable (x) is provided. $$\begin{array} { l l } y & x \\4 & 2 \\3 & 1 \\4 & 4 \\6 & 3 \\8 & 5\end{array}$$
SSE = 6
SST = 16

The least squares estimate of the y-intercept is

A) 1.
B) 2.
C) 3.
D) 4.

Question 74

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$$ The least squares estimate of the slope or b₁ equals

A) 1.
B) -1.
C) -11.
D) 11.

Question 75

Regression analysis was applied between sales (y in $1000) and advertising (x in $100) and the following estimated regression equation was obtained. $\hat { y }$ = 80 + 6.2x

Based on the above estimated regression line, if advertising is $10,000, then the point estimate for sales (in dollars) is

A) $62,080.
B) $142,000.
C) $700.
D) $700,000.

Question 76

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. $$\begin{array} { l } \widehat { y } = 12 + 1.8 x \\n = 17 \\\mathrm { SSR } = 225 \\\mathrm { SSE } = 75 \\\mathrm {~s} b _ { 1 } = .2683\end{array}$$
Based on the above estimated regression equation, if advertising is $3000, then the point estimate for sales (in dollars) is

A) $66,000.
B) $5412.
C) $66.
D) $17,400.

Question 77

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$$ The least squares estimate of the slope or b₁ equals

A) 1.
B) -1.
C) 6.
D) -5.

Question 78

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\12 & 4 \\3 & 6 \\7 & 2 \\6 & 4\end{array}$$
The coefficient of determination equals

A) -.4364.
B) .4364.
C) -.1905.
D) .1905.

Question 79

Regression analysis was applied between sales data (y in $1000s) and advertising data (x in $100s) and the following information was obtained. $$\begin{array} { l } \widehat { y } = 12 + 1.8 x \\n = 17 \\\mathrm { SSR } = 225 \\\mathrm { SSE } = 75 \\\mathrm {~s} b _ { 1 } = .2683\end{array}$$ The F statistic computed from the above data is

A) 3.
B) 45.
C) 48.
D) 50.

Question 80

You are given the following information about y and x. $$\begin{array} { l l } \text { Dependent Variable } ( y ) & \text { Independent Variable } ( x ) \\5 & 1 \\4 & 2 \\3 & 3 \\2 & 4 \\1 & 5\end{array}$$ The coefficient of determination equals

A) 0.
B) -1.
C) +1.
D) -.5.