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Chapter 3: Q 34. (page 175)
If we leave out the low outlier, the correlation for the remaining 13 points in the preceding figure is closest to
a. −0.95.
b. −0.65.
c. 0.
d. 0.65.
e. 0.95.
The correct option is (d)
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Stand mixers The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers.35 The mixer from Walmart (highlighted in red) was much lighter—and cheaper than the other mixers.
a. Describe what influence the highlighted point has on the equation of the least-squares regression line.
b. Describe what influence the highlighted point has on the standard deviation of the residuals and r2
Will I bomb the final? We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of Pomona College looked at the exam scores of all students who took his statistics class over a 10-year period. 17 The least-squares line for predicting final-exam score from midterm-exam score was . Octavio scores 10 points above the class mean on the midterm. How many points above the class mean do you predict that he will score on the final? (This is an example of the phenomenon that gave “regression” its name: students who do well on the midterm will on the average do less well, but still above average, on the final.)
The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable to be the percent change in a stock market index in January and the response variable to be the change in the index for the entire year. We expect a positive correlation between and y because the change during January contributes to the full year’s change. Calculation from data for an 18-year period gives
(a) What percent of the observed variation in yearly changes in the index is explained by a straight-line relationship with the change during January?
(b) For these data, Explain what this value means
Using data from the LPGA tour, a regression analysis was performed using x = average driving distance and y = scoring average. Using the output from the regression analysis shown below, determine the equation of the least-squares regression line.
a. y^=87.974+2.391x
b. y^=87.974+1.01216x
c. y^=87.974−0.060934x
d. y^=−0.060934+1.01216x
e. y^=−0.060934+87.947x
More Starbucks In Exercises 6 and 12, you described the relationship between fat (on Page Number: 204 grams) and the number of calories in products sold at Starbucks. The scatterplot shows this relationship, along with two regression lines. The regression line for the food products (blue squares) is y^=170+11.8x. The regression line for the drink products
(black dots) is y^=88+24.5x
a. How do the regression lines compare?
b. How many more calories do you expect to find in a food item with 5 grams of fat compared to a drink item with 5 grams of fat?
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