Scatterplot, linear correlation coefficient, regression equation

Goal: You will construct a scatterplot, find a linear correlation coefficient, and regression equation.

The attached data set includes unemployment rate, inflation rate, presidential approval and consumer confidence rating (reference number is 1964). You will be investigating the relationship between Consumer Confidence Index and Presidential approval by answering the questions below.

1. Using Excel or Google Sheets, construct a scatter plot showing the relationship between consumer confidence and presidential approval. Once complete, take a screenshot and paste it into this document.

2. Interpret the graph. That is, do you see a strong correlation? Is it positive or negative? Explain what a positive vs. a negative correlation means in the context of this problem.

3. Find and interpret the linear correlation coefficient r. By interpret, I mean to state whether the numerical value confirms or refutes the strength and sign of the correlation that you discussed in problem 2.

4. State the equation for the linear regression.

5. Clearly interpret the slope of the regression equation. That means to use complete sentences to specifically describe what the slope means in this context, in word.

6. Use your regression to estimate presidential approval for the consumer index of 80.

7. What percentage of variation in Presidential Approval can be explained by Consumer Confidence? (Note: this is something I only mentioned very briefly in class, but it is the value of r2, and it is referred to as the Coefficient of Determination.)

8. Based on the value of r2, is your model good for predicting presidential approval rating?

9. Do you see any outliers in the data? If yes, state x and y coordinates of the point(s).

10. If there is an outlier, remove it, compute r for the new data. Did the correlation coefficient increase or decrease? Explain why. If you removed any outliers, for which president did they occur?

No matter how you personally feel about Donald Trump, he does have the lowest term-average approval rating in recorded history. His average approval rating was just 41%, and he left office with only 34% approval rating. The average consumer confidence during his term was 93.1, while it was 80.7 when he left office. How accurately does your model predict both Trump's term-average approval rating and his approval rating upon leaving office? Explain at least two major factors affected consumer confidence and/or Trump's approval rating by the end of his term.