Below is the script for questions 6.1 and 6.2 and they both have questions for A,B,C,D.

For both parts below, imagine a researcher proposes that a linear relationship exists between the amount of money a person earns and their happiness. They believe that income (X) predicts happiness scores (Y). The researcher collects income and happiness data and finds that the average income is $63,000, with a standard deviation of $20,000, and the happiness scale has a mean of 6.9, with a standard deviation of 3. (Read each section carefully, different subsections ask for different information.

6.1. Imagine the observed correlation between income and happiness is r = .00. If the researcher were to estimate parameters and evaluate their linear model, what would be the values of (a) the a and b parameters of the model, (b) error variance of the model and (c) R2 for the model. (d) What would this value of R2 say about how good of a job this model is doing? (e) If you were to plot a regression line through the data, what would it look like (either describe it in words or sketch a scatter plot with a regression line).

6.2. Imagine the observed correlation between income and happiness is r = 1. If the researcher were to estimate parameters and evaluate their linear model, what would be the values of (a) error variance and (b) R2 be for the model? (c) What would this value of R2 say about how good of a job this model is doing? (d) If you were to plot a regression line through the data, what would it look like (either describe it in words or sketch a scatter plot with a regression line).