I need help woth question d through g 4. A multiple regression analysis between
ID: 3311784 • Letter: I
Question
I need help woth question d through g
4. A multiple regression analysis between yearly income (Y in $1,000s), college grade point average (X), age of the individuals (X2), and the gender of the individual (X; zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained Coefficients Standard Error 14400 16512 0.1225 14400 Intercept 4.0928 10.0230 0.1020 4.4811 X2 X3 Residual (Error 23.91 a. Write the estimated regression equation for the result above. b. Interpeet the meaning of the coefficient of Xj. c. Compute the coefficient of determination (r. d. Is the coefficient of Xi significant? Use = 0.05. e. Is the coefficient of X-significant? Use = 0.05. f. Is the coefficient of X, significant? Use = 0.05. g. Perform an F test and determine whether or not the model is significant.Explanation / Answer
here total sample size n=10 ; degree of freedom for t test =n-p =10-4 =6
for 6 degree of freedom and 0.05 level critical value of t =2.447
Deciison rule : reject null hypothesis if test statistic t<-2.447 or t>2.447
d)
for test statistic t =coefficient/std error ==10.023/1.6512=6.070
as test statistic is in critical region ; reject null hypothesis and conclude that X1 is significant
e)
test statistic t =coefficient/std error =0.1020/0.1225 =0.833
as test statistic is not in critical region ; fail to reject null hypothesis and conclude that X2 is not significant
f)
test statistic t =coefficient/std error =-4.4811/1.44=-3.112
as test statistic is in critical region ; reject null hypothesis and conclude that X3 is significant
g)for 0.05 level and 3,6 degree of freedom critical value F =4.757
reject null hypothesis if test statistic F >4.757
completing above ANOVA table:
as test statistic 30.16 is higher then critical value ; threfore model is signfiicant
df SS MS F regression 3 360.59 120.20 30.16 residual 6 23.91 3.99 total 9 384.5