Please use the given printout and answer the following questions. SUMMARY OUTPUT
ID: 3127593 • Letter: P
Question
Please use the given printout and answer the following questions.
SUMMARY OUTPUT Rearession Statistics Multiple F R Square Adjusted R Square Standard Error Observations 0.9630 0.9274 0.9129 1.5510 7 ANOVA df Significance F MS Regression Residual Total 153.7199 153.7199 63.8974 0.0005 12.0287 2.4057 6 165.7486 Coefficients 17.9276 1.0946 Standard Error P-value Upper 95% 8.0490 1.4466 Lower 95% Intercept Income Rate ($1000) tstat 10.1053 -1.7741 0.1362 0.1369 7.9936 0.0005 Lower 95.0% -43.9042 0.7426 Upper 95.0% 8.0490 1.4466 -43.9042 0.7426Explanation / Answer
a) here b0 means the intercept of the regression line. so from tha table b0=17.9276
b) here b1 means the slope of the regression line. so from the table b1=-1.0946
c) b1 here is the slope. it denotes the amount of increase of the response variable if the predictor is increased by one unit.
say the regression equation be y=b0+b1*x
now the predictor is increased by one unit (x+1) then the response be y1
so y1=b0+b1*(x+1)
so increase in response= y1-y=b0+b1*(x+1)-b0+b1*x=b0+b1*x+b1-b0+b1*x=b1
hence b1 denotes the amount of increase of the response variable if the predictor is increased by one unit. [answer]
d) so the regression line is
y=b0+b1*x
or, y=17.9276-1.0946*x where x is the predictor and y is the response [answer]
e) coefficient of determination is R2 . from the table R2=0.9274=92.74%
f) coefficient of correlation is Multiple R. from the table Multiple R is 0.9630
g) coefficient of determination denotes the amount of the total variability of the response is explained by the regression equation.
here R2=92.74% which means 92.74% of the total variability of the response is explained by the regression equation.
h) correlation coefficient measures the extent to which the predictor and the response are linearly dependent.
here multiple R=0.9630
which means that the predictor and the response are highly positively linearly related