Review Exercises (week 13: Correlation and Regression)

Review Exercises ( week 13: Correlation and Regression)

In Exercises 1 and 2, organize the data in a scatter plot. Then find the sample correlation coefficient, r. Determine whether there is a positive linear correlation, negative linear correlation, or no linear correlation between the variables. What can you conclude?

1. The ages of eight cows (in years) and their milk production (in gallons) per week

Age, x
Milk production, y	37.0	35.4	33.3	33.1	32.3	33.7	30.2	29.6

1. The annual per capita sugar consumption (in kilograms) and the average number of cavities of 11- and 12-yer-old children in seven countries:

Sugar, x	2.1	5.0	6.3	6.5	7.7	8.7	11.6
Cavities, y	0.59	1.51	1.55	1.70	2.18	2.10	2.43

In Exercises 3 and 4, use the given sample statistics to test the claim about the population correlation, ρ, at the indicated level of significance α for the given sample statistics.

1. Claim: ρ = 0, α = 0.10. Sample statistics: r = 0.24, n = 26.
2. Claim: ρ ≠ 0, α 0.05. Sample statistics: r = -0.55, n = 22.

In Exercises 5 and 6, test the claim about the population correlation coefficient, ρ, at the indicated level of significance α. Then interpret the decision in the context of the original claim.

1. Refer to the data in Exercise 1. At α = 0.05, test the claim that there is a linear correlation between a cow’s age and milk production.

1. Refer to the data in exercise 2. Is there enough evidence to conclude that there is no linear correlation between sugar consumption and tooth decay?

In Exercises 7 and 8, use the data to find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Can you make a guess about the sign and magnitude of r? Calculate r and check your guess.

1. The heights in inches of adult brothers and sisters from nine families.

Sister, x
Brother, y

1. The engine displacement (in cubic inches) and the fuel economy (in miles per gallon) of seven automobiles.

Displacement, x
Fuel efficiency, y	29.5	34.5	23.0	17.0	33.5	23.0	15.5

In Exercises 9 and 10, use the regression equations found in Exercise 7 and 8 to predict the value of y for each value of x, if meaningful. If not, explain why not.

1. Refer to exercise 7. What height would you predict for a male whose sister is

(a) 61 in.?

(b) 66 in.?

(c) 71 in.?

1. Refer to Exercise 8. What fuel efficiency rating would you predict for a car with an engine displacement of

(a) 86 in. ?

(b) 198 in. ?

(c) 289 in. ?

(d) 407 in. ?

In Exercises 11 – 14, use the value of the linear correlation coefficient, r, to find the coefficient of determination. Interpret the result.

1. r = - 0.553

1. r = - 0.962

1. r = 0.181

1. r = 0.740

In Exercises 15 and 16, use the data to

(a) find the coefficient of determination, , and interpret the result with regard to the regression line, and

(b) find the standard error of estimate, , and interpret the result.

1. The following table shows the area of eight living spaces (in square feet) and the cooling capacity (in Btu per hour) of the air conditioners used in those spaces. The regression equation is

Living area, x
Cooling capacity, y	10,200

1. The following table shows the prices of 16 gas grills (in U.S. dollars) and their usable cooking area (in square inches). The regression equation is

Area, x
Price, y

Area, x
Price, y

In Exercises 17 – 20, construct the indicated prediction intervals.

1. Construct a 90% prediction interval fir the height of a brother in Exercise 7 whose sister is 64 inches tall.

1. Construct a 90% prediction interval for the fuel efficiency of an automobile in Exercise 8 that has an engine displacement of 265 cubic inches.

1. Construct a 95% prediction interval for the cooling capacity of an air conditioner in Exercise 15 that is used in a living g area of 720 square feet.

1. Construct a 95% prediction interval for the price of a gas grill in Exercise 16 with a usable cooking area of 400 square inches.

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