Question

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.)

  YˆY^ =  −  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 good fit.
	This model has a poor fit.

Answer 1

Answer:

Below is a regression using

x=average price

y=units sold

n=20 stores

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

intercept t=b1-0 /    sb1   = 614.93 / 51.23623 = 12.002

slop 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 poor fit.

Thank you!