Answer:
Check the explanation
Step-by-step explanation:
[tex]S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=52120800[/tex]
[tex]S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=21.74[/tex]
[tex]S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=-31284[/tex]
Slope of the regression equation is
[tex]b_{1}=\frac{S_{xy}}{S_{xx}}=-1439.01[/tex]
and intercept of the equation will be
[tex]b_{0}=\frac{1}{n}(\sum y - b_{1} \sum x)=28818.00[/tex]
So the regression equation will be
y'=28818.00-1439.01x
C.
the attached images below comprise of the output of the regression analysis generated by excel:
Intercept:
Hypotheses are:
[tex]H_{0}:\beta_{0}=0,H_{a}:\beta_{0}\neq 0[/tex]
t-value of intercept is 8.820
P-value is 0.0000
Since p-value is less than 0.05 so intercept is significant to the model.
Slope:
Hypotheses are:
[tex]H_{0}:\beta_{1}=0,H_{a}:\beta_{1}\neq 0[/tex]
t-value of intercept is -7.12
P-value is 0.0000
Since p-value is less than 0.05 so slope is significant to the model.
D.
Since from regression output R-square is 0.864 so 86.4% of the variation in the prices of the bicycles is accounted for by the weight of bicycles.
E.
For X= 15 estimated y value is
y'=28818.00-1439.01*15 = 7232.85
hence, required predicted price is $7232.85.
