12. Regression

Using the Queens data and the results from Problem 3, complete the following:

b. Interpret the slope and y-intercept, if applicable.

2018 Senate ElectionA major theme during the 2018 election in both the House and Senate was the popularity of President Trump (a Republican). The scatter diagram below shows the presidential approval rating (percent of registered voters who approve of the job the president is doing) versus the percentage of votes received by the Democratic senatorial candidate in the 2018 election.

c. The least-squares regression equation, where presidential approval (x) is the predictor and percent Democrat (y) is the outcome, is: ŷ = -0.9147x + 94.9933. Interpret the slope. What does this suggest about Senate candidates from the president's party?

Analyzing a Newspaper ArticleA Chicago Tribune article claimed that school districts with higher poverty levels have shorter school days.

b. The least-squares regression line for length, y, and income, x, is y^=−0.0102x+7.11. Explain the meaning of the slope for this regression line. Should the y-intercept be interpreted? If it makes sense, interpret it.

Problems 17–22 use the results from Problems 27–32 in Section 4.1.

[DATA] Home Runs (Refer to Problem 31, Section 4.1.) The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game.

b. Explain the meanings of the slope and y-intercept in this context, if appropriate.

[DATA] Graduation Rates Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_2_28 using the file format of your choice for the version of the text you are using. The variable “Cost” represents the four-year cost including tuition, supplies, room and board. The variable “Annual ROI” represents the return on investment for graduates of the school. It essentially represents how much you would earn on the investment of attending the school. The variable “Grad Rate” represents the graduation rate of the school.  

b. Interpret the slope.

[DATA] Graduation Rates Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_2_28 using the file format of your choice for the version of the text you are using. The variable “Cost” represents the four-year cost including tuition, supplies, room and board. The variable “Annual ROI” represents the return on investment for graduates of the school. It essentially represents how much you would earn on the investment of attending the school. The variable “Grad Rate” represents the graduation rate of the school.  

e. Interpret the slope

Using the data from Problem 1:

b. Explain the meaning of the slope and y-intercept, if appropriate.