Using the data from Problem 1:
b. Explain the meaning of the slope and y-intercept, if appropriate.

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 sample data below, run a hypothesis test on $\beta$ to see if there is evidence that there is a positive correlation between $x$ and $y$ with $\alpha =0.01$.

Using the sample data below, create a confidence interval for $\beta$ to see if there is evidence that there is a positive correlation between $x$ and $y$ with $\alpha =0.01$.

You Explain It! Study Time and Exam Scores

After the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam score. She found that a linear relation exists between the two variables. The least-squares regression line that describes this relation is:

ŷ = 6.3333x + 53.0298

b. Interpret the slope.

Bull Markets A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data to the right represent the number of months and percentage change in the S&P 500 (a group of 500 stocks) during the 25 bull markets dating back to 1929 (the year of the famous market crash).

e. Interpret the slope.