Search for question
Question

# Part 2 - Simple Linear Regression

In this lab we'll be looking at data from all 30 Major League Baseball teams in 2011 and examining the linear relationship between runs scored in a season and the number of at- bats for each time. Our aim will be to summarize this relationship both graphically and numerically in order to determine if the number of at-bats helps us predict a team's runs scored in a season.

For this part of the assignment, please refer to the DA8_ SLR.R script and the mlb.csv file available on the Canvas page for this assignment. Be sure to read through all comments in the R script to understand how we visualize and fit the least squares regression line in R.

1. (1 point) We are interested in determining if the number of at-bats is a good predictor of the number of runs a team scores in the 2011 season. Identify the explanatory and response variables for this question of interest.

2. (2.5 points) Using the R script, construct a scatterplot of the at-bat and runs variables. Paste your plot below. Using the scatterplot, describe the relationship between the number of at-bats and runs. Include the strength, direction, and form of the relationship. Comment on whether or not there are any outliers present in the data.

3. (0.5 points) Calculate and report the correlation coefficient between the two quantitative variables.

4. (2 points) Using the Im() and summary() functions provided to you in the R script, fit the least squares regression line that models the linear relationship between the number of at-bats and the number of runs scored. Write out the estimated least squares regression model. (Hint: your answer should be in the form = bo + b₂x where bo and b₁ are replaced with the estimates for the intercept and slope.

5. (1 point) Interpret the slope estimate in the context of the problem.

6. Using the R script, construct a plot of the residuals for this model.

a. (1 point) Paste your residual plot below.

b. (1.5 points) Use the residual plot to assess whether the conditions are met: linearity, normality in the response values, and constant variance about the regression line. Comment on whether or not you think each of these conditions are met and use the residual plot to support your comments.

7. (1 point) Suppose a team expects 5,600 at-bats in one season. Use the least squares regression line you reported in question 4 to predict the number of runs the team will score.

8. (1 point) Suppose the team in question 7 actually scores 728 runs in the season. Compute the residual for this team.

9. (1 point) Now suppose that a new team is joining the MLB and only expects 4,900 at- bats in the season. Why is inappropriate to use this model to predict this team's runs scored?