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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.