Based on my expertise in statistics, here are the answers to the multiple choice questions:
Question 2:
The correct answer is: it will be the same regardless of which variable is the x and which is the y.
Pearson's correlation coefficient r is a symmetric measure, meaning it does not depend on which variable is considered x and which is y. The value of r remains unchanged if you swap the variables.
Question 3:
The correct answer is: 75.4% of the variation in the response variable can be explained by our knowledge of the explanatory variable.
An R-squared of 0.754 means 75.4% of the variation in the response variable is accounted for by the explanatory variable through the linear regression model.
Question 7:
The correct answer is: are randomly distributed around the line y - ŷ = 0
If the residuals plotted against the x-values show a random scatter around the zero line, it indicates the data fit the linear pattern well.
Question 9:
The correct answer is: The value of the correlation coefficient will move closer to 0.
Adding an outlier will reduce the strength of the correlation between the two variables.
Question 15:
The correct answer is: The r squared is greater than 0.50
If correlation r is 0.50, the R-squared must be greater than 0.50 since R-squared is the square of the correlation r.