3. Multiple Linear Regression [20 points] Use R to perform a multiple linear regression on the data provided in "Hwk3 Hospital Infection data.cav". Infection risk ("InfetRsk") is the dependent variable; length of stay ("Stay"), age of subject ("Age"), and number of X-Rays performed at the hospital ("Xray") are the independent variables, which we are interested in investigating to see if they can explain infection risk. (Note: the data file also contains other variables that will not be used in this exercise.) a) Estimate a constant (intercept term), as well as the coefficients for all three explanatory variables noted above. and provide the final regression line equation. Show the complete results from the R summary() function. b) From the results given, show how you would reject the null hypothesis of no relation between infection risk and any of the variables above. c) Based on your results, which explanatory variables are statistically significant? Provide the null and alternate hypotheses you are testing and summarize the test using the R results for each variable. d) Using an R function (show results), provide a 95% confidence interval for each of the three coefficients. Based on these confidence intervals, make an inference about the significance of each variable. Do these results agree with your conclusions in part c)? e) If not all of the explanatory variables had statistically significant coefficients, re-do your analysis with only those that were statistically significant. Using the resulting regression equation (or your original equation, if all coefficients were statistically significant), estimate the mean infection risk of a $5-year-old subject who stays for 12 days at a hospital that performs 85 X-Rays