4 Hot hearts An experimenter was interested in the relationship between temperature and heart rate in the common grass frog. The temperature was manipulated in 2-degree increments ranging from 2 to 180 C with heart rates 2 recorded at each temperature in beats per minute. (A different, randomly selected, frog was used at each temperature.) In this question we will look at a simple linear regression of heart rate (y) on temperature (I). Temp 2 4 6 8 10 12 14 16 18 Heart rate 5 11 10 13 22 23 30 28 32 A) Draw (or create in R) a scatter plot of heart rate versus temperature. B) Compute the least squares estimates of the slope and intercept for the regression line. C) Compute the ANOVA table by giving the sources of variation, df, SS, and MS. D) Perform an F test for Ho : B1 = 0 vs HA : B1 # 0. E) Compute a 95% confidence interval for So and compute a 95% confidence interval for 81. F) Compute R' and give an interpretation. G) Suppose the temperature is I. = 11C. Estimate the population mean heart rate corresponding to this temperature, i.e. Yest, and give a 90% confidence interval for this estimate. H) Consider again heart rate corresponding to a temperature of r. = 11 C. Suppose a single grass frog is to be observed once at this temperature. Predict the heart rate in this situation (i.e. give Ypred) and give a 90% confidence interval for this prediction. How does this confidence interval compare to the confidence interval in part (g)? I) Compute the fitted values and the residuals. Make a residual plot by plotting the residuals versus the fitted values. Comment on the residual plot. J) Make a normal quantile comparison plot (normal QQ plot) of the residuals, and comment