Question

. Question 3 (p) egresion analyis regress weight length mate () sS 23 Number of obs Fi 2,20 38.s Prob R-squared Source 1S Model 4688 63921 2 244.31511 Residuat1537.1958720 76.8597937 e,7s32 Total 6225.8269 22 282 Root PtSE weight 195s Conf. Intervati Coef sd ErI 6791132 .995297ธ 1515773 6.57 0.00 . ele8.953177 3.8878 2.38 .932 cons -108.9868 25.66558-4 . 25 ล.900-162 , 5242-55.449,1

Answer 1

a.
Number of obs = 23
23 observations were used to run the regression to achieve the given output.

F(2, 20) = 30.50
Critical value of F statistic at numerator degree of freedom = 2 and denominator degree of freedom = 20 is 30.50
The test statistic of F test should be greater than this critical value for the model to be statistically significant.

Prob > F = 0.0000
The p-value of F test is 0.0000. Thus, the regression model is statistically significant.

R-squared = 0.7531
This is R-squared value of the model.The given model explains 75.31% of the variation of the person's weight.

Adj R-squared = 0.7284
This is adjusted R-squared value of the model.The given model explains 72.84% of the variation of the person's weight after adjusting for number of predictors in the model.

Root MSE = 8.767
Standard error of the regression is 8.767. The average distance that the observed values fall from the regression line is 8.767

b.
Test statistic, t = (Coefficient) / Standard error)
degree of freedom = df for residual = 20
P-value P[t] = P(t > Test statistic) for df = 20
Critical value of t at 95% confidence interval and df = 20 is tc = 20.86
95% confidence interval is,
(Coefficient - tc * standard error, Coefficient + tc * standard error_

c.
The difference in change of weight for male and female for a unit change in length is the coefficient of male*length (0.0750441)
The significance of the coefficients changed because there is significant interaction between male and length.
We can conduct F test to compare both models and determine whether the interaction term male*length is significant in the model.
Test statistic is F = [(RSS_R - RSS_UR) / q ] / [RSS_UR / (n-k)] with df = q, n-k
where RSS_R, RSS_UR are SS Residual for model without male*length term and with male*length term respectively.
q = 1 (as the number of restricted variable (male*length ) is 1)
n = 23 (number of observations)
k = 3 (number of predictors in the full model with male*length term)