Write the formula for each t statistic and verify the t statistics shown below.
ID: 3360731 • Letter: W
Question
Write the formula for each t statistic and verify the t statistics shown below. (Round your answer to 3 decimal places. Negative values should be indicated by a minus sign.)
(c)
State the degrees of freedom for the t tests and find the two-tail critical value for t by using Appendix D. (Round t.025 value to 3 decimal places.)
Use Excel's function =T.DIST.2T(t, d.f.) to verify the p-value shown for each t statistic (slope, intercept). (Round your answer to 4 decimal places.)
The percentage of variation in units sold that can be explained by average price is %. (Round your answer to 3 decimal places.)
Below is a regression using X = average price, Y = units sold, n = 20 stores.Explanation / Answer
a) Yhat= -109.112X+ 614.930
b) t statistic of slope= beta1/std.error of x = -109.112/51.3623= -2.124(verified)
t statistic of intercept= beta0/std error of intercept= 614.930/51.234= 12.002 (verified)
c) Degrees of freeedom of t = (n-2)= (20-2)=18
critical value of t (0.25) with d.f= 18 is 2.100
d) p value for intercept is < .00001. The result is significant at p < .05.
p value for slope is .04778.The result is significant at p < .05.
e1) t2 for slope = beta1/ Std error of x =-109.112/51.363= -2.124
p value of t (-2.124)=0.048
F = 4.51
p value for F is 0.048
Since p value of F= pvalue of t(slope)
This implies F=t2
e2) R^2= 1- SSE/SST= 1-12288.31/15369.20
R^2= 1-0.799= 0.20045
e3) The percentage of variation in units sold that can be explained by average price is 20.045%
f) This model has poor fit as R^2 is very small.
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