8.8 Scatter Plots, Correlation, and Regression Lines

For each of the following pairs of related datasets, identify which (if any) should be assigned the role of response variable and which should be assigned to be the explanatory variable.

1. A person’s height and weight
2. A professional basketball player’s salary and their average points scored per game (which is a measure of how good they are at basketball)
3. The length and width of leaves on a tree

The data that were plotted in the previous example can be found in the dataset “correlationcoefficient1”. All of them share the same values for the explanatory variable $x$. The four responses are labeled $y 1$ through $y 4$. Compute the correlation coefficients for each, if appropriate, using Google Sheets. Round to the nearest hundredth.

Suppose you have datasets $x$ and $y$ with the following statistics: $x$ has mean 21 and standard deviation 4, $y$ has mean 8 and standard deviation 2, and their correlation coefficient is −0.4. What’s the equation of the regression line?

In the example, we considered the relationship between goals scored (GF) and goals against (GA) using the dataset “NHL19”. Recreate the scatter plot in Google Sheets, and use it to find the equation of the regression line.

The data in “MLB2019Off” gives offensive team stats for the 2019 Major League Baseball season. Use that dataset to answer the following questions:

1. What is the equation of the regression line for runs (R) vs. hits (H)?
2. How many runs would we expect a team to score if the team got 1500 hits in a season?
3. Did the Kansas City Royals (KCR) overperform or underperform in terms of runs scored, based on t…

The data in “WNBA2019” gives team statistics from the 2019 WNBA season. Use that dataset to answer these questions about team wins (W) and the proportion of team field goals made (FG%, the number of shots made divided by the number of shots attempted. Even though this column is labeled using a percent sign, the values are not expressed as percentages):

1. What is the equation of the regression line…