Question: Consider the n = 11 data values in the following table.
Suppose we consider the simple normal linear regression to describe the relationship between the response Y and the predictor X.
(a) Plot the data in a scatter plot.
(b) Calculate the least-squares line and plot this on the scatter plot in part (a).
(c) Plot the standardized residuals against X(d) Produce a normal probability plot of the standardized residuals.
(e) What are your conclusions based on the plots produced in parts (c) and (d)?
(f) If appropriate, calculate 0.95-confidence intervals for the intercept and slope. (g) Construct the ANOVA table to test whether or not there is a relationship between the response and the predictors. What is your conclusion?
(h) If the model is correct, what proportion of the observed variation in the response is explained by changes in the predictor?
(i) Predict a future Y at X = 00 Is this prediction an extrapolation or an interpolation? Determine the standard error of this prediction.
(j) Predict a future Y at X= 60 Is this prediction an extrapolation or an interpolation? Determine the standard error of this prediction.
(k) Predict a future Y at X = 200 Is this prediction an extrapolation or an interpolation? Determine the standard error of this prediction. Compare this with the standard errors obtained in parts (i) and (j) and explain the differences.