Write the formula for each t statistic and verify the t statistics shown below.
ID: 3229094 • 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. R2 0.200 Std. Error 26.128 n 20 ANOVA table Source SS df MS F p-value Regression 3,080.89 1 3,080.89 4.51 .0478 Residual 12,288.31 18 682.68 Total 15,369.20 19 Regression output confidence interval variables coefficients std. error t (df = 18) p-value 95% lower 95% upper Intercept 614.9300 51.2343 12.002 .0000 507.2908 722.5692 Slope 109.1120 51.3623 2.124 .0478 217.0202 1.2038 (a) Write the fitted regression equation. (Round your answer to 3 decimal places. Negative values should NOT be indicated by a minus sign.) = X (b)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.)
t Intercept Slope(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.)
df t.025 ± (d)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.)
p-value Intercept Slope (e-1) Calculate t2 for slope and show that F = t2. (Round your answer to 3 decimal places.) F = t2 (e-2) Calculate R2. (Round your answer to 3 decimal places.) R2 (e-3)The percentage of variation in units sold that can be explained by average price is %. (Round your answer to 3 decimal places.)
(f) Choose the option that best describes the fit of this regression. This model has a poor fit. This model has a good fit.Explanation / Answer
a) we know that the regression equation is given by y=a+bx
from above analysis
y=614.93 -109.112(average price)
b) we use t test with n-2 df
slope t=b1-0 / sb1 = 614.93 / 51.23623 = 12.002
intercept t = b0-0 / sb0 = -109.112 / 51.23626= -2.124
c) degrees of freedom = n-2
20-2=18
two tailed critical value =2.101 from t table
d) Use Excel's function =T.DIST.2T(t, d.f.)
T DIST(2.124 ,18,2) = 0.0477 (SLOPE)
T DIST (12.002,18,2) = 0.000(INTERCEPT )
e)
e - 1: F = t2 = (-2.124)2 = 4.511
e - 2: R2 = 0.200
e - 3: The percentage of variation in units sold that can be explained by average price is 20%
f: This model has a good fit.
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