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Chapter 3: Q 40. (page 203)
Residual gas Refer to Exercise 38. During March, the average temperature was 46.4°F and Joan used an average of 490 cubic feet of gas per day. Calculate and interpret the residual for this month.
Residual is
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Calculating achievement a study found a strong link between the number of calculators possessed by high school pupils and their arithmetic proficiency, according to the principle of a high school. Based on this study, he decides to buy each student at his school two calculators, hoping to improve their math achievement. Explain the flaw in the principal’s reasoning.
More Olympic athletes In Exercises 5 and 11, you described the relationship between height (in inches) and weight (in pounds) for Olympic track and field athletes. The scatterplot shows this relationship, along with two regression lines. The regression line for the shotput, hammer throw, and discus throw athletes (blue squares) is y^=−115+5.13x. The regression line for the remaining athletes (black dots) is y^=−297+6.41x
a. How do the regression lines compare?
b. How much more do you expect a 72-inch discus thrower to weigh than a 72-inch sprinter?
Predicting wins Earlier we investigated the relationship between x =
payroll (in millions of dollars) and y = number of wins for Major League Baseball teams in 2016. Here is a scatterplot of the data, along with the regression line y^=60.7+0.139x
a. Predict the number of wins for a team that spends \(200 million on payroll.
b. Predict the number of wins for a team that spends \)400 million on payroll.
c. How confident are you in each of these predictions? Explain your reasoning.
Olympic figure skating For many people, the women’s figure skating competition is the highlight of the Olympic Winter Games. Scores in the short program x and scores in the free skate y were recorded for each of the 24 skaters who competed in both rounds during the 2010 Winter Olympics in Vancouver, Canada.28 Here is a scatterplot with least-squares regression line y^=−16.2+2.07x. For this model, s = 10.2 and r2 = 0.736.
Movie candy Is there a relationship between the amount of sugar (in grams) and the number of calories in movie-theater candy? Here are the data from a sample of 12 types of candy: 
a. Sketch a scatterplot of the data using sugar as the explanatory variable.
b. Use technology to calculate the equation of the least-squares regression line for predicting the number of calories based on the amount of sugar. Add the line to the scatterplot from part (a).
c. Explain why the line calculated in part (b) is called the “least-squares” regression line.
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