Problem 6.2 One hundred restaurants were selected from the area of Westwood, Brentwood, and Santa Monica and some information were gathered about them. The data is for year 2000 and is from http://ww.zegat.com. It can be accessed at http: Hm . stat .ucla . edu/ 'nchristo/statisticleOC/restaurant .txt There are four variables, with ratings on the scale 1-30 (best=30): Variable Description :31 food Food rating. 2:2 decor Decor rating. 2:3 ser Service rating. 1; cost Cost (3) for dinner including one drink and the tip. Consider a multiple regression model y = 50 + 2;] j$j+ for predicting the cost. As usual, let ,3 = [30, . . . , 33F be the LSE of ,6. Assume the error e is normal. (a) Find the standard error of the S1 2,33. (b) Use a ttest to test for 51 = 2,63 at level 5%. (c) Predict the cost for a resturant with avarage ratings :c = [15, 15,15]T, and build a 95% condence interval for it. (d) Find the sampling (joint) distribution of [52, .51 233]?" E R2. Leave 0'3 as unknown. (e) Find the correlation coefcient between 5'1 and $3. (f) Find c E R such that $1 653 is independent of 53