Providedetailed reasoning why or why not Regression is appropriate using just

Practice Problems:  Chapter 12 

(part E is worth 3 points--all other parts of the question are worth 1 point)

1) A)  Providedetailed reasoning why or why not Regression is appropriate using just the scatterplot and correlation given below.  

B) Given the Regression Equation below indicate the explanatory variable and the response variable.

C)  What is the y-intercept?  Does the y-intercept have any logical interpretation?    We cannot logically interpret the y-intercept unless we have data points at X = 0 in the data set.   If in fact we cannot logically interpret the y-intercept, then the y-intercept is only useful for positioning the line properly in the plot.    So, the question hinges on whether we have data points at X=0 in the data set.  

D) What is the slope coefficient?  What is the slope interpretation?   Be specific  (ie:  for each unit increase in ____, we expect _____ to increase/decrease by _____).

E)What is the predicted Tax value for a house of size 2,000 square feet?  Show all work.

F) From the output below can we conclude that size is a significant linear predictor of real estate taxes?   In answering this question, first provide the null and alternative hypothesis being tested.   Then, calculate the test statistic using the values in the output (show all work).   Finally, indicate the p-value of our test statistic and the conclusion and reasoning behind your conclusion.

G) The R² value is 54.5%.   Provide a detailed description of what an R² of 54.5% indicates.

H) What are the FIT (fitted values) and what are the RESI (Residuals)?  Be specific.

I) Describe why we use a Residuals vs Fitted Values scatterplot to test for constant variance.   (see figure 12.4 in the text)   Remember, the fitted values (the values on the line) are the mean Y values for the given X value and we expect the observed Y values to be equally distributed around each and every X value.

J) Given the Residuals vs Fitted values scatterplot below is the constant variance assumption appropriate?

K) Why do we want the Residuals to be normally distributed? 

Given the Probability Plot below are these Residuals normally distributed?

L)  Given the X value of 2,500 square feet--you are given a 95% confidence interval for μ_y and a prediction interval.   What do each of these indicate?