Question: Tests were carried out to determine the effect of gas inlet temperature (degrees Fahrenheit) and rotor speed (rpm) on the tar content (grains/cu ft) of a gas stream, producing the following data

Suppose we consider the normal linear regression model to describe the relationship between Y (tar content) and the predictors W (rotor speed) and X (temperature).

(a) Plot the response in scatter plots against each predictor.

(b) Calculate the least-squares equation.

(c) Plot the standardized residuals against W and 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 regression coefficients.

(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 predictors?

(i) In an ANOVA table, assess the null hypothesis that there is no effect due to Wgiven that X is in the model.