I. (7 pts) You are given the following estimated equation: 145.85+30.83nprevist
ID: 3325494 • Letter: I
Question
I. (7 pts) You are given the following estimated equation: 145.85+30.83nprevist -1.814 age-23396unmarried birthweight = 3 Std. Errors (67.98) (2.917) (2.133) (27.79) n=3000 R-squared:0.0758 Where the variables are described as follows: birthweight = the weight of the newborn, in grams; nprevist the number of prenatal visits during pregnancy; age = the age of the newborn's mother; unmarried = l if the newborn's mother is unmarried, and 0 otherwise. a. b. c. Provide an interpretation for each partial slope estimate in this equation. (3pts) Are the explanatory variables individually significant at 5%? (3 pts) Are all the explanatory variables jointly significant at 5%? (1pt)Explanation / Answer
(a) The equation is as follows :
birthweight = 3145.85 + 30.83*nprevist -1.814*age -233.9*unmaried
This means the y intercept of this regression line is at 3145.85. for every unit increase in nprevist, birthweight will increase by 30.83 grams, for every unit icrease in age of the mother, birthweight will decrease by 1.814 gms, and if the mother is unmarried, wt will lesser by233 gms
(b) Now t value is given by t = b1/sb1 = 30.83/2.91 for nprevist, -1.81/2.133 for age and 233.9/27.79 for being married or unmarried
Now if the p values generated by these t scores are less than 0.05 they are all indiviually significant at 5%
This can be looked up in any std. t dist table
(c) Yes, all the expanatory variables are not ointly significant at 5 % as the Rsquared value is very low, the model only explains about 7% of the total variability in the data. So together they are not significant.