Question

1) Consider the following computer output from a regression analysis. The regression equation is Y = 12.9 + 2.34 x Predictor Coef SE Coef T P Constant 12.857 1.032 ? ? X 2.3445 0.1150 ? ? S = 1.48111 R-sq = 98.1% R-sq(adj) = 97.9% Analysis of Variance Source DF SS MS F P Regression 1 912.43 912.43 ? ? Residual error 8 17.55 ? Total 9 929.98 a) Write down the null and alternative hypotheses for intercept and slope. b) Calculate the T statistic and p-values in the Predictor table. (no need to calculate the exact p-value, just state if p-value is bigger than alpha=0.05 or smaller than alpha=0.05. c) Write down the hypothesis tested in ANOVA output F-test d) Find the missing values of MSE, F statistic and p-value in the ANOVA table. e) Can you conclude that this linear regression model defines a useful relationship between response(y) and predictor variable X (in other words, test the significance of regression). Which part of the output did you use to make this conclusion? f) What percentage of the variability in response variable (y) is explained by this regression model? a. Which metric did you use to answer this question? b. Show how this metric is calculated using SS values. c. What percentage of the variability in response is due to random error? g) Build a 95% CI on slope parameter (??).

          1) Consider the following computer output from a regression analysis.
The regression equation is
Y = 12.9 + 2.34 x
Predictor Coef SE Coef T P
Constant 12.857 1.032 ? ?
X 2.3445 0.1150 ? ?
S = 1.48111 R-sq = 98.1% R-sq(adj) = 97.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 912.43 912.43 ? ?
Residual error 8 17.55 ?
Total 9 929.98
a) Write down the null and alternative hypotheses for intercept and slope.
b) Calculate the T statistic and p-values in the Predictor table. (no need to calculate the exact p-value, just state if p-value is bigger than alpha=0.05 or smaller than alpha=0.05.
c) Write down the hypothesis tested in ANOVA output F-test
d) Find the missing values of MSE, F statistic and p-value in the ANOVA table.
e) Can you conclude that this linear regression model defines a useful relationship between response(y) and predictor variable X (in other words, test the significance of regression). Which part of the output did you use to make this conclusion?
f) What percentage of the variability in response variable (y) is explained by this regression model?
a. Which metric did you use to answer this question?
b. Show how this metric is calculated using SS values.
c. What percentage of the variability in response is due to random error?
g) Build a 95% CI on slope parameter (??).

1) Consider the following computer output from a regression analysis.
The regression equation is
Y = 12.9 + 2.34 x
Predictor Coef SE Coef T P
Constant 12.857 1.032 ? ?
X 2.3445 0.1150 ? ?
S = 1.48111 R-sq = 98.1% R-sq(adj) = 97.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 912.43 912.43 ? ?
Residual error 8 17.55 ?
Total 9 929.98
a) Write down the null and alternative hypotheses for intercept and slope.
b) Calculate the T statistic and p-values in the Predictor table. (no need to calculate the exact p-value, just state if p-value is bigger than alpha=0.05 or smaller than alpha=0.05.
c) Write down the hypothesis tested in ANOVA output F-test
d) Find the missing values of MSE, F statistic and p-value in the ANOVA table.
e) Can you conclude that this linear regression model defines a useful relationship between response(y) and predictor variable X (in other words, test the significance of regression). Which part of the output did you use to make this conclusion?
f) What percentage of the variability in response variable (y) is explained by this regression model?
a. Which metric did you use to answer this question?
b. Show how this metric is calculated using SS values.
c. What percentage of the variability in response is due to random error?
g) Build a 95% CI on slope parameter (??).

Added by Rachel P.

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