TOTALS: (m) Give an equation for and calculate the Fstatistic in the ANOVA test
ID: 3239146 • Letter: T
Question
TOTALS:
(m) Give an equation for and calculate the Fstatistic in the ANOVA test of H(there is no linear relationship between x & y) versus H(there exists a linear relationship between x & y). Calculate the degrees of freedom df for this Fstatistic. Use Excel to calculate the corresponding pvalue. (n) Give an equation for and calculate the estimated standard deviation of the slope s(b). (o) Give an equation for and calculate the tstatistic to test H( = 0) vs H( 0). Calculate the degrees of freedom for this tstatistic. Use Excel to calculate the corresponding pvalue. (p) Write the sample regression equation again in the following format: y = b + bx (tstatistic)*** n = ?; r² = ?; r²(adj) = ?; F = ? [pvalue] This format is typically presented in a report’s main text. In addition, the corresponding table of full regression results can be put in the appendix. For the number of stars besides the tstatistic, use this rule: *** for pvalue 0.01; ** for 0.01< pvalue 0.05; * for 0.05 < pvalue 0.1.
obs x y x^2 xy 1 6.95 8.56 48.30250 59.49200 2 4.70 6.71 22.09000 31.53700 3 5.13 9.67 26.31690 49.60710 4 8.67 5.63 75.16890 48.81210 5 2.48 8.52 6.15040 21.12960 Total 27.93000 39.09000Explanation / Answer
F=1.0656
p=0.377
p>0.05
Fail to reject Null hypotehsis
ACcept null hypothesis
there is sufficient evidence to conclude
there is no linear relationship between x & y
Model is not significant
regression equation is
y=9.792-0.3534x
slope=-0.3534
y intercept=9.792
r=0.512
correlation coeffcient=r=0.512
moderate positive relationship exists between x and y.
r sq=0.2621=26.21% variation in y is explained by model.
not a good model
t=-1.0323
SUMMARY OUTPUT Regression Statistics Multiple R 0.511966 R Square 0.262109 Adjusted R Square 0.016146 Standard Error 1.606155 Observations 5 ANOVA df SS MS F Significance F Regression 1 2.749077 2.749077 1.065643 0.377861 Residual 3 7.739203 2.579734 Total 4 10.48828 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 9.792092 2.042775 4.793525 0.017271 3.29107 16.29311 x -0.3534 0.342342 -1.0323 0.377861 -1.44289 0.736086Related Questions
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