Deck 14: Simple Linear Regression

Question 1

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

A) confidence interval
B) prediction interval
C) residual interval
D) correlation interval

Answer 1

confidence interval

Question 2

The difference between the observed value of the dependent variable and the value predicted by using the estimated regression equation is called _____.

A) the standard error
B) a residual
C) a prediction interval
D) the variance

Answer 2

a residual

Question 3

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 6,000 units
D) decrease by 3,000 units

Answer 3

decrease by 3,000 units

Question 4

In a simple regression analysis (where y is a dependent and x an independent variable), if the y-intercept is positive, then it must be true that _____.

A) there is a positive correlation between x and y
B) there is a negative correlation between x and y
C) if x is increased, y must also increase
D) None of the answers is correct.

Question 5

In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.

A) horizontal band of points centered near 0
B) widening band of points
C) band of points having a slope consistent with that of the regression equation
D) parabolic band of points

Question 6

In regression analysis, the independent variable is typically plotted on the _____.

A) y-axis of a scatter diagram
B) x-axis of a scatter diagram
C) y-axis of a histogram
D) x-axis of a histogram

Question 7

The least squares criterion is _____.

A) min $\sum \left( x _ { i } - y _ { i } \right) ^ { 2 }$
B) min $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 }$
C) min $\left( \sum y _ { i } - \hat { y } _ { i } \right) ^ { 2 }$
D) min $\sum \left( y _ { i } - \hat { y } _ { i } \right) ^ { 2 }$

Question 8

A procedure used for finding the equation of a straight line that provides the best approximation for the relationship between the independent and dependent variables is ______.

A) correlation analysis
B) the mean squares method
C) the least squares method
D) the most squares method

Question 9

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) None of the answers is correct.

Question 10

A measure of the strength of the relationship between two variables is the _____.

A) confidence interval estimate
B) slope b₁ of the estimated regression line
C) standard error of the estimate
D) correlation coefficient

Question 11

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), 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 12

As the goodness of fit for the estimated regression equation increases, the _____.

A) absolute value of the regression equation's slope increases
B) value of the regression equation's y-intercept decreases
C) value of the coefficient of determination increases
D) value of the correlation coefficient increases

Question 13

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 unit of currency
C) can be any units
D) cannot be in dollars

Question 14

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) None of the answers is correct.

Question 15

Application of the least squares method results in values of the y-intercept and the slope that minimizes the sum of the squared deviations between the _____.

A) observed values of the independent variable and the predicted values of the independent variable
B) actual values of the independent variable and the predicted values of the dependent variable
C) observed values of the dependent variable and the predicted values of the dependent variable
D) None of the answers is correct.

Question 16

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

Question 17

A least squares regression line ______.

A) may be used to predict a value of y if the corresponding x value is given
B) implies a cause-effect relationship between x and y
C) can only be determined if a good linear relationship exists between x and y
D) All of the answers are correct.

Question 18

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

A) dependent variable
B) independent variable
C) intervening variable
D) None of the answers is correct.

Question 19

Regression analysis was applied between sales (in $1000s) and advertising (in $100s), and the following regression function 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 20

In a regression analysis, the variable that is used to predict the dependent variable ______.

A) must have the same units as the variable doing the predicting
B) is the independent variable
C) is the dependent variable
D) usually is denoted by x

Question 21

In a regression analysis, if r² = 1, then _____.

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

Question 22

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

A) much larger than 1, if the correlation is positive
B) much smaller than 1, if the correlation is negative
C) either much larger than 1 or much smaller than 1
D) None of the answers is correct.

Question 23

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ? $\hat { y}$ = 50,000 ? 8x
?
The above equation implies that an increase of _____.

A) $1 in price is associated with a decrease of $8 in sales
B) $8 in price is associated with an increase of $8,000 in sales
C) $1 in price is associated with a decrease of $42,000 in sales
D) $1 in price is associated with a decrease of $8,000 in sales

Question 24

If the coefficient of determination is a positive value, then the regression equation _____.

A) must have a positive slope
B) must have a negative slope
C) could have either a positive or a negative slope
D) must have a positive y-intercept

Question 25

If a data set has SST = 2,000 and SSE = 800, then the coefficient of determination is _____.

A) .4
B) .6
C) .5
D) .8

Question 26

In simple linear regression, r² is the _____.

A) estimated regression equation
B) coefficient of correlation
C) sum of the squared residuals
D) coefficient of determination

Question 27

If the coefficient of correlation is .4, the percentage of variation in the dependent variable explained by the estimated regression equation _____.

A) is 40%
B) is 16%
C) is 4%
D) can be any positive value

Question 28

Which of the following is correct?

A) SSE = SSR + SST
B) SSR = SSE + SST
C) SST = SSR + SSE
D) SST = (SSR)²

Question 29

A regression analysis between sales (y in $1000) and advertising (x in dollars) resulted in the following equation: $\hat { y }$ = 50,000 + 6x ?
The above equation implies that an increase of _____.

A) $6 in advertising is associated with an increase of $6,000 in sales
B) $1 in advertising is associated with an increase of $6 in sales
C) $1 in advertising is associated with an increase of $56,000 in sales
D) $1 in advertising is associated with an increase of $6,000 in sales

Question 30

It is possible for the coefficient of determination to be _____.

A) larger than 1
B) less than 1
C) less than 0
D) All of the answers are correct, depending on the situation under consideration.

Question 31

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

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

Question 32

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 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 line can be computed
C) y-intercept can be computed
D) All of the answers are correct.

Question 34

If the coefficient of correlation is .8, then the percentage of variation in the dependent variable explained by the estimated regression equation is _____.

A) 0.80%
B) 80%
C) 0.64%
D) 64%

Question 35

In a regression analysis, if r² = 1, then _____.

A) SSE must also be equal to 1
B) SSE must be equal to 0
C) SSE can be any positive value
D) SSE must be negative

Question 36

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

A) .667
B) .600
C) .400
D) 1.500

Question 37

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

A) .35
B) .65
C) 2.85
D) .45

Question 38

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

A) .600
B) .166
C) 1.666
D) .375

Question 39

SSE can never be _____.

A) larger than SST
B) smaller than SST
C) equal to 1
D) equal to 0

Question 40

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 41

The standardized residual is provided by dividing each residual by its _____.

A) mean residual
B) corresponding x value
C) standard deviation
D) z-score

Question 42

The numerical value of the coefficient of determination ______.

A) is always larger than the coefficient of correlation
B) is always smaller than the coefficient of correlation
C) is negative if the coefficient of determination is negative
D) can be larger or smaller than the coefficient of correlation

Question 43

An observation that has a strong effect on the regression results is called a(n) _____.

A) residual
B) sum of squares error
C) influential observation
D) None of the answers is correct.

Question 44

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation.

Question 45

A data point (observation) that does not fit the trend shown by the remaining data is called a(n) _____.

A) residual
B) outlier
C) point estimate
D) None of the answers is correct.

Question 46

In regression analysis, which of the following is NOT a required assumption about the error term ε?

A) The expected value of the error term is 0.
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) All are required assumptions about the error term.

Question 47

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) Not enough information is given.

Question 48

If the coefficient of determination is .81, then the coefficient of correlation _____.

A) is .6561
B) must be 0.9
C) must be positive
D) None of the answers is correct.

Question 49

Data points having high leverage are often _____.

A) residuals
B) sum of squares error
C) influential
D) None of the answers is correct.

Question 50

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

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

Question 51

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) None of the answers is correct.

Question 52

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of seven weeks follows. Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation and the coefficient of determination. ​

Question 53

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of seven weeks follows. Use Excel's Regression tool to construct a residual plot and use it to determine if any model assumptions have been violated. ​

Question 54

If the coefficient of correlation is a positive value, then the slope of the regression line _____.

A) must also be positive
B) can be either negative or positive
C) can be 0
D) None of the answers is correct.

Question 55

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel's Regression tool to construct a residual plot and use it to determine if any model assumptions have been violated.

Question 56

The primary tool or measure for determining whether the assumed regression model is appropriate is _____.

A) the F test
B) residual analysis
C) the r² value
D) the correlation coefficient

Question 57

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to develop a scatter diagram and to compute the least squares estimated regression equation and the coefficient of determination.

Question 58

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel to

Question 59

A company has recorded data on the weekly sales for its product (y) and the unit price of the competitor's product (x). The data resulting from a random sample of seven weeks follows. Use Excel to ​

Question 60

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

A) must also be negative
B) must be 0
C) can be either negative or positive
D) must be positive

Question 61

Part of an Excel output relating x (independent variable) and y (dependent variable) is shown below. Fill in all the blanks marked with a question mark. ​ ​ ​

Question 62

Given below are seven observations collected in a regression study on two variables, x (independent variable) and y (dependent variable). Use Excel's Regression tool to construct a residual plot and use it to determine if any model assumptions have been violated.

Question 63

Coyote Cable has been experiencing an increase in cable service subscribers in recent months due to increased advertising and an influx of new residents to the region. The number of subscribers (in 1000s) for the last 16 months is as follows: ​
Using simple linear regression, forecast the number of subscribers for months 17, 18, 19, and 20.

Question 64

Part of an Excel output relating x (independent variable) and y (dependent variable) is shown below. Fill in all the blanks marked with a question mark. ​ ​ ​