In order to fit the linear regression that explains y = "sleeping time" (variable sleep, in hours per week) in terms of r= "working time" (variable work, in hours per week), data on n = 700 individuals was collected. Some summary statistics of the collected data are shown below: *x = 24980 9 = 38430 = 1060000 *19; = 1333.000 (a) Calculate the intercept and the slope of the regression of interest. (5p.) (b) Predict the number of hours sleeping for a person working forty hours per week. (5p.) A second explanatory variable =-{ if the ith individual has kids younger than 3 0 otherwise I2i = (variable young kid) was added to the model. The estimated coefficients and their estimated standard errors are shown in the following table. Intercept work young kid Coefficients 59.80 -0.1507 -13.82 Standard Error 0.6561 0.0168 47.33 (c) Using a significance level of 5%, test the hypothesis that young kid is significant in the model. (5p.) (d) Interpret the three estimated coefficients. (5p.)