Deck 4: Correlation and Linear Regression

Question 1

Linear regression was used to describe the trend in world population over time.Below is a plot of the residuals versus predicted values.What does the plot of residuals suggest?

A)An outlier is present in the data set.
B)The linearity condition is not satisfied.
C)A high leverage point is present in the data set.
D)The data are not normal.
E)The equal spread condition is not satisfied.

Answer 1

The linearity condition is not satisfied.

Question 2

A company studying the productivity of its employees on a new information system was interested in determining if the age (X) of data entry operators influenced the number of completed entries made per hour (Y).The regression equation is
)Suppose the actual completed entries per hour for an operator who is 35 years old was 8.The residual is _______ .

A)-1.3
B)2.6
C)-3.5
D)1.3
E)-2.2

Answer 2

-1.3

Question 3

Shown below is a correlation table showing correlation coefficients between stock price, earnings per share (EPS) and price/earnings (P/E) ratio for a sample of 19 publicly traded companies.Which of the following statements is false?
Correlations: Stock Price, EPS, PE

A)EPS is the best predictor of stock price.
B)The strongest correlation is between EPS and stock price.
C)There is a weak negative association between PE and EPS.
D)PE is the best predictor of stock price.
E)The weakest correlation is between PE and EPS.

Answer 3

PE is the best predictor of stock price.

Question 4

Data were collected on monthly sales revenues (in $1,000s) and monthly advertising expenditures ($100s) for a sample of drug stores.The regression line relating revenues (Y) to advertising expenditure (X) is estimated to be
)The correct interpretation of the slope is that for each additional ____________________________ .

A)$1 spent on advertising, predicted sales revenue increases by $9,000
B)$100 spent on advertising, predicted sales revenue increases by $9,000
C)$100 spent on advertising, predicted sales revenue decreases by $9,000
D)$1,000 in sales revenue, advertising expenditures decrease by $48.30
E)$100 in sales revenue, advertising expenditures decrease by $48.30

Question 5

A supermarket chain gathers data on the amount they spend on promotional material (e.g., coupons, etc.) and sales revenue generated each quarter.The predictor variable is ________________________ .

A)sales revenue
B)amount spent on promotional material
C)number of coupons offered
D)supermarket chains
E)none of the above.

Question 6

A consumer research group examining the relationship between the price of meat (per pound) and fat content (in grams) gathered data that produced the following scatterplot.

If the point in the lower left hand corner (2 grams of fat; $3.00 per pound) is removed, the correlation would most likely ________________________ .

A)remain the same
B)become positive
C)become weaker negative
D)become stronger negative
E)become zero

Question 7

Based on the following residual plot, which condition / assumption for linear regression is not satisfied?

Border line missing for graph

A)Linearity.
B)Quantitative Variables.
C)Equal Spread.
D)Outlier.
E)None of the above; all conditions are satisfied.

Question 8

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month.

Based on the summary statistics shown below, what percent of the variability in the number of pounds of coffee sold per week can be explained by price?

A)95.47%
B)100%
C)85.9%
D)55.6%
E)4.68%

Question 9

A company studying the productivity of their employees on a new information system was interested in determining if the age (X) of data entry operators influenced the number of completed entries made per hour (Y).The regression equation is
)If s_x=14.04 and s_y=2.61, then the correlation coefficient between age and productivity is ____ .

A).779
B)-.236
C).575
D)-.929
E)-.779

Question 10

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month.

Based on the scatterplot, the linear relationship between number of pounds of coffee sold per week and price is ________________________ .

A)strong and positive
B)strong and negative
C)weak and negative
D)weak and positive
E)nonexistent

Question 11

For the following scatterplot,

The likely correlation coefficient is ________________________ .

A)+0.35
B)+0.90
C)+0.77
D)-0.89
E)-1.00

Question 12

Data were collected on monthly sales revenues (in $1,000s) and monthly advertising expenditures ($100s) for a sample of drug stores.The regression line relating revenues (Y) to advertising expenditure (X) is estimated to be
)The predicted sales revenue for a month in which $1,000 was spent on advertising is ______________ .

A)$50,000
B)$851.70
C)$8,951.70
D)$41,700
E)$90,000

Question 13

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month.

Based on the data and summary statistics, the intercept of the estimated regression line that relates the response variable (monthly sales) to the predictor variable (price per pound) is ______________ .

A)95.459
B).858
C)-4.684
D)-.858
E)-8.999

Question 14

Suppose the correlation, r, between two variables x and y is -0.44.What percentage of the variability in y cannot be explained by x?

A)19%
B)44%
C)81%
D)88%
E)12%

Question 15

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month.Based on the scatterplot shown below, which of the following statements is true?

A)The quantitative variable condition is satisfied.
B)The linearity condition is satisfied.
C)There are no obvious outliers.
D)All of the above.
E)None of the above.

Question 16

Suppose the correlation, r, between two variables x and y is -0.44.What would you predict about a y value if the x value is 2 standard deviations above its mean?

A)It will be .88 standard deviations below its mean.
B)It will be .88 standard deviations above its mean.
C)It will be 2 standard deviations below its mean.
D)It will be .44 standard deviations below its mean.
E)It will be .44 standard deviations above its mean.

Question 17

The scatterplot shows monthly sales figures (in units) and number of months of experience for a sample of salespeople.

The correlation between monthly sales and level of experience is most ________________________ .

A)-.235
B)0
C).180
D)-.914
E).914

Question 18

The scatterplot shows monthly sales figures (in units) and number of months of experience for a sample of salespeople.

The association between monthly sales and level of experience can be described as ________________________ .

A)positive and weak
B)negative and weak
C)negative and strong
D)positive and strong
E)nonlinear

Question 19

A study examined consumption levels of oil and carbon dioxide emissions for sample of counties.The response variable in this study is ________________________ .

A)oil
B)oil consumption
C)carbon dioxide emissions
D)countries
E)none of the above.

Question 20

A small independent organic food store offers a variety of specialty coffees.To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month.

Based on the data and summary statistics shown below, the slope of the estimated regression line that relates the response variable (monthly sales) to the predictor variable (price per pound) is ________________________ .

A)95.459
B).858
C)-4.681
D)-.858
E)-8.999

Question 21

The disadvantage of re-expressing variables is that ________________________ .

A)we have to explain the association in terms of the transformed variables
B)we cannot use the standard regression models
C)it is not commonly used
D)it can be difficult
E)A and D