Draw a sketch diagram to show the relationship between the Regression Sum of Squares, the Residual Sum of Squares and the Total Sum of Squares for one observation that is not on the estimated regression line

Use the information from the ANOVA table to test if R2 =0. Explain whether this is the same as testing the coefficient on temperature equals to zero or not.

22. [35 marks] The Hamilton City Council (HCC) is very concerned about the amount of water that is required by Hamilton residents in the hot summer months. Data has been collected on water use W, in millions of litres and on daily temperatures 7, in centigrade, for 15 days in January 2019. The following Excel Output (with two deliberate omissions) show the results from a simple regression that can be used to predict the amount of water required by Hamilton residents depending on expected temperature for that day. SUMMARY OUTPUT Regression Statistics Multiple R 0.91 R Square A Adjusted R Square 0.81 Standard Error 6.68 Observations 15 ANOVA Significance df SS MS F F Regression 1 2667.2 2667.2 59.7 3.2591E-06 Residual 13 580.6 44.7 Total 14 3247.7 Standard Upper Lower Upper Coefficients Error t Stat P-value Lower 95% 95% 99.0% 99.0% Intercept 15.6 6.7 2.3 0.036 1.203 30.077 -4.49 35.77 Temp 2.1 0.3 B 3.26E-06 1.541 2.736 1.305 2.972