Chapter 7 mid-term test bank practice PDF

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1 Copyright © 2014 Pearson Canada Inc.Business Statistics, Cdn. 2e (Sharpe) Chapter 7: Introduction to Linear RegressionShort Answer - Quiz AConsider the following to answer the question(s) below:To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data we...

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Business Statistics, Cdn. 2e (Sharpe) Chapter 7: Introduction to Linear Regression Short Answer - Quiz A Consider the following to answer the question(s) below: To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. The data, scatterplot and summary statistics are shown below. ANNUAL PAY $ 70,609 $ 58,487 $ 104,561 $ 43,922 $ 82,613 $ 116,250 $ 76,751 $ 68,513 $ 137,000 $ 94,469

CASH BONUS $ 11,225 $ 6,238 $ 14,194 $ 4,188 $ 11,863 $ 13,671 $ 7,758 $ 20,760 $ 55,000 $ 34,368

Mean Standard Deviation

$ 85,318 $ 28,077

$ 17,927 $ 15,618

Correlation

0.735

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1) Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative variable condition. b. Linearity condition. c. Outlier condition. Answer: a. Yes, both variables are quantitative. b. Yes, appears straight enough. c. Yes, no obvious outliers. L.O.: 1 2) Estimate the linear regression model that relates the response variable (cash bonus) to the predictor variable (annual pay). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model. Answer: a. 0.409 b. -16945 c. Cash Bonus = -16,945 + 0.409 (Pay) L.O.: 1 3) Find the value of R2. Interpret its meaning in this context. Answer: 0.54, which means that 54% of the variability in cash bonuses can be explained by pay. L.O.: 2 4) Using the regression equation, a. Estimate the cash bonus for an executive at Johnson Financial earning $82,613 a year. b. What is the residual for this estimate? What does it mean? Answer: a. $16,844. b. -$4,981. It tells us that the actual bonus was $4,981 less than the model predicts. L.O.: 1 5) Use the regression equation to answer the following questions. a. Estimate the cash bonus for an executive at Johnson Financial earning $200,000 a year. b. How confident should you be in this estimate? Explain. Answer: a. $64,855. b. Not very since we are predicting for a value of pay beyond the range of the data. We should be careful about extrapolating beyond the range of x values. L.O.: 1

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6) Below is a plot showing residuals versus fitted values for the estimated regression equation relating cash bonus to pay for the account executives at Johnson Financial. Are all the conditions for linear regression met? Explain.

Answer: The residual plot shows that the equal spread condition is violated. The residuals "fan out" from left to right in a cone shape. L.O.: 1

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Short Answer - Quiz B Consider the following to answer the question(s) below: 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 kilograms of each variety of coffee were sold last month. The data, scatterplot, and summary statistics are shown below. PRICE PER KILOGRAM $ 3.99 $ 5.99 $ 7.00 $ 12.00 $ 4.50 $ 7.50 $ 15.00 $ 10.00 $ 12.50 $ 8.99

KILOGRAMS SOLD 75 60 65 45 80 70 25 35 40 50

Mean Standard Deviation

$ 8.75 $ 3.63

54.50 18.33

Correlation

-0.927

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1) Comment on whether each of the following conditions for correlation / linear regression is met. a. Quantitative variable condition. b. Linearity condition. c. Outlier condition. Answer: a. Yes, both variables are quantitative. b. Yes, appears straight enough. c. Yes, no obvious outliers. L.O.: 1 2) Estimate the linear regression model that relates the response variable (monthly sales) to the predictor variable (price per kilogram). a. Find the slope of the regression line. b. Find the intercept of the regression line. c. Write the equation of the linear model. Answer: a. -4.684 b. 95.47 c. kilograms sold = 95.47 -4.684 Price per kilogram L.O.: 1 3) Find the value of R2. Interpret its meaning in this context. Answer: 0.858, which means that 85.8% of the variability in the number of kilograms of coffee sold per month is explained by price. L.O.: 2 4) Use the estimated regression equation to answer the following questions. a. Estimate the monthly sales for a variety of coffee that costs $12.00 per kilogram. b. What is the residual for this estimate? What does it mean? Answer: a. 39.26 kilograms b. 5.74 kilograms. It tells us that the actual monthly sales were 5.74 kilograms more than the model predicts. L.O.: 1 5) Use the estimated regression equation to answer the following questions. a. Estimate the monthly sales for a variety of coffee that costs $20.00 per kilogram. b. How confident should you be in this estimate? Explain. Answer: a. 1.79 kilograms b. Not very since we are predicting for a value of pay beyond the range of the data. We should be careful about extrapolating beyond the range of x values. L.O.: 1

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6) Below is a plot showing residuals versus fitted values for the estimated regression equation relating monthly sales of coffee to price per kilogram. Are all the conditions for linear regression met? Explain.

Answer: The residual plot indicates that all conditions are reasonably met although a slight spreading is noted. L.O.: 1

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Multiple Choice - Quiz C Consider the following to answer the question(s) below: To determine whether the cash bonuses paid by Johnson Financial Group are related to annual pay, data were gathered for 10 account executives who received such bonuses in 2007. The data, scatterplot and summary statistics are shown below. ANNUAL PAY CASH BONUS $ 70,609 $ 11,225 $ 58,487 $ 6,238 $ 104,561 $ 14,194 $ 43,922 $ 4,188 $ 82,613 $ 11,863 $ 116,250 $ 13,671 $ 76,51 $ 7,758 $ 68,513 $ 20,760 $ 137,000 $ 55,000 $ 94,469 $ 34,368 Mean Standard Deviation

$ 85,318 $ 28,077

Correlation

0.735

$ 17,927 $ 15,618

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1) The slope of the estimated regression line that relates the response variable (cash bonus) to the predictor variable (annual pay) is A) 0.409 B) -16945 C) 0.54 D) 3.45 E) none of the above Answer: A L.O.: 1 2) The intercept of the estimated regression line that relates the response variable (cash bonus) to the predictor variable (annual pay) is A) 0.409 B) -16945 C) 0.54 D) 3.45 E) none of the above Answer: B L.O.: 1 3) What percent of the variability in cash bonuses can be explained by pay? A) 100% B) 85% C) 73% D) 30% E) 54% Answer: E L.O.: 2 4) Based on the estimated regression line, the cash bonus for an executive at Johnson Financial earning $82, 613 a year would be A) $11,863 B) $16,844 C) $27,682 D) $4,958 E) $15,819 Answer: B L.O.: 1

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5) The residual for the estimated cash bonus of an executive at Johnson Financial earning $82, 613 a year would be A) $0 B) -$4,981 C) -$15,819 D) -$4,958 E) $15,819 Answer: B L.O.: 1 Consider the following to answer the question(s) below: 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 kilograms of each variety of coffee were sold last month. The data, scatterplot and summary statistics are shown below. PRICE PER KILOGRAM $ 3.99 $ 5.99 $ 7.00 $ 12.00 $ 4.50 $ 7.50 $ 15.00 $ 10.00 $ 12.50 $ 8.99

KILOGRAMS SOLD 75 60 65 45 80 70 25 35 40 50

Mean Standard Deviation

$ 8.75 $ 3.63

54.50 18.33

Correlation

-0.927

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6) Which of the following statements is true? A) The quantitative variable condition is not satisfied. B) The linearity condition is not satisfied. C) There are obvious outliers. D) The quantitative variable condition is satisfied. E) The Y-intercept of the line of best fit is approximately zero. Answer: D L.O.: 1 7) The slope of the estimated regression line that relates the response variable (monthly sales) to the predictor variable (price per kilogram) is A) 95.47 B) 0.858 C) -4.684 D) -0.858 E) -8.999 Answer: C L.O.: 1 8) The intercept of the estimated regression line that relates the response variable (monthly sales) to the predictor variable (price per kilogram) is A) 95.47 B) 0.858 C) -4.684 D) -0.858 E) -8.999 Answer: A L.O.: 1 10 Copyright © 2014 Pearson Canada Inc.

9) What percent of the variability in the number of kilograms of coffee sold per month can be explained by price? A) 95.47% B) 100% C) 85.8% D) 55.6% E) 4.68% Answer: C L.O.: 2 10) Below is a plot showing residuals versus fitted values for the estimated regression equation relating monthly sales of coffee to price per kilogram. Based on this plot we can say

A) The linearity condition is not satisfied. B) The linearity condition is reasonably satisfied. C) A slight thickening of the plot is definitely not evident. D) The correlation coefficient is close to one. E) Nothing related to regression analysis can be said based on this graph. Answer: B L.O.: 1

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11) A regression on a pair of variables, x and y, results in the value of R2 equal to 0.7834. Which of the following statements is true? A) The correlation between x and y must be 0.7834. B) The correlation between x and y must be -0.8851. C) The correlation between x and y must be -0.7834. D) The correlation between x and y must be either 0.8851 or -0.8851. E) The correlation between x and y must be 0.8851. Answer: D L.O.: 2 12) A pair of variables, x and y, have a correlation coefficient of -0.8851. Which of the following statements is true? A) x explains about 78.34 percent of the variation in y. B) x explains about 88.51 percent of the variation in y. C) y explains about 78.34 percent of the variation in x. D) x cannot explain about 78.34 percent of the variation in y. E) y explains about 88.51 percent of the variation in x. Answer: A L.O.: 2

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Consider the following to answer the question(s) below: To determine whether the tip left at the end of a meal is related to the size of the total bill at their restaurant, Chez Michelle, data were gathered for 10 customers. The data and summary statistics are shown below. Total Bill $126 $58 $86 $20 $59 $120 $14 $17 $26 $74

Tip $19 $11 $20 $3 $14 $30 $2 $4 $2 $16

Mean Standard deviation

$60 41.57

$12 9.45

Correlation

0.937

13) The slope of the estimated regression line that relates the response variable (tip) to the predictor variable (total bill) is A) 0.2128 B) -0.2128 C) 0.8773 D) 0.9366 E) -0.9367 Answer: A L.O.: 1 14) The intercept of the estimated regression line that relates the response variable (tip) to the predictor variable (total bill) is A) -0.6684 B) 57.42 C) 0.6684 D) 0.5950 E) none of these Answer: A L.O.: 1

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15) The percentage of the variability in tips that can be explained by the total bill is A) 87.7% B) 93.7% C) 21.3% D) 66.8% E) 96.8% Answer: A L.O.: 2 16) The regression equation would predict what size of tip if the total bill was $120? A) $24.87 B) $15.55 C) $26.03 D) $30.00 E) $20.62 Answer: A L.O.: 1 17) The residual for the estimated tip for a total bill of $120 would be A) $5.13 B) $19.00 C) 0 D) -$11.45 E) $9.38 Answer: A L.O.: 1 18) If a residual plot exhibits a curved pattern in the residuals, this means that A) The relationship between x and y is also curved. B) The residuals are not normally distributed. C) x and y are positively correlated. D) The residuals have a constant variance. E) The relationship between x and y is linear. Answer: A L.O.: 1 19) Which of the following is a correct interpretation for the regression slope coefficient b1? A) The average change in y of a one-unit change in x will be b1 units. B) For a one-unit change in y, we can expect the value of the independent variable to change by b1 units on average. C) For each unit change in x, the dependent variable will change by b1 units. D) The average change in x of a one-unit change in y will be b1 units. E) The change in y of a one-unit change in x will always be b1 units. Answer: A L.O.: 1

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20) A manufacturing company is interested in predicting the number of defects (y) that will be produced each hour on the assembly line (x). Using sample data they estimate the equation as defects = 5.67 + 0.048 (hours). Which of the following statements is true? A) The correlation between x and y is positive. B) 4.8% of the variability in y is explained by x. C) 23.08% of the variability in y is explained by x. D) An increase in x of one-unit will result in an average increase of 5.67 in y. E) The relationship between x and y could be either positive or negative. Answer: A L.O.: 1

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