MATH 533 Week 6 Homework Problems/Solutions (Summer 2019)
- Question 11.2.21-T: The average during distance (yards) and driving accuracy (percent of drives that land in the fairway) for 8 golfers are recorded in the table to the right. Complete parts a through e below.
- Question 11.2.22-T: One manufacturer has developed a quantitative index of the “sweetness” of orange juice. (The higher the index, the sweeter the juice). Is there a relationship between the sweetness index and a chemical measure such as the amount of water-soluble pectin (parts per million) in the orange juice. Data collected on these two variables for 24 production runs at a juice manufacturing plant are … in the accompanying table. Suppose a manufacturer wants to use simple linear regression to predict the sweetness (y) from the amount of pectin (x).
- Question 11.4.43: Use the following pairs of observations to construct an 80% and a 98% confidence interval for β1.
- Question 11.4.55-T: If you pay more in attention to go to a top business school, will it necessarily result in a higher probability of a job offer at graduation? Let y = percentage of graduates with job offers and x = tuition cost, then fit the simple linear model, E(y) = β0 + β1x, to the data below. Is there sufficient evidence (at α = 0.10) of a positive linear relationship between y and x?
- Question 11.5.62 T: Construct a scattergram for each data set. Then calculate r and r2 for each data set, interpret their values. Complete parts a through d.
- Question 11.5.63: Each week coaches in a certain football league face a decision during the game. On fourth-down, should the team punt the ball or go for a first-down? To aid in the decision-making process, statisticians at a particular university developed a regression model for predicting the number of points scored (y) by a team that has a first-down with a given number of yards (x) from the opposing goal line. One of the models fit to data collected on five league teams from a recent season was the simple linear regression model, E(y) = β0 + β1 The regression yielded the following results: ŷ = 4.02 – 0.43x, r2 = 0.15. Complete parts a and e below.
- Question 11.5.63: A group of researchers developed a new method for ranking the total during performance of golfers on a tour. The method requires knowing a golfer’s average during distance (yards) and during accuracy (percent of drives that land in the fairway). They construct a straight-line model relating during accuracy (y) to during distance (x). A MINITAB printout with prediction and confidence intervals for a driving distance of x = 300 is shown below.
- Question 11.6.90: The accompanying data in the table below were … from life tests for two different brands of cutting tools. Complete parts a through c.
- Question 11.7.92-T: To study how social media may influence the products consumers buy, researchers collected the opening weekend box office revenue (in million of dollars) for 23 recent movies and the social media message rate (average number of messages referring to the movie per hour). The data are available below. Conduct a complete simple linear regression analysis of the relationship between revenue (y) and message rate (x).
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