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# Write Regression Equation, State Degrees of Freedom, Compute

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Instructions:
? Write the regression equation
? State degrees of freedom and compute critical value
? Conclusion about slope
? Interpret confidence limits for slope
? Verify that F = square of t
? Describe fit of regression

It might be expected that baseball teams with better batting averages also score more homeruns. Let's examine that thought. The regression table below, produced by Excel's Analysis ToolPak, shows the result of a regression analysis using Major League Baseball data from the 2007 season. The independent variable (X) is team batting average and the dependent variable (Y) is homeruns per game.

Regression Statistics
Multiple R 0.0427
R Square 0.0018
Adjusted R Square -0.0338
Standard Error 0.1903
Observations 30

ANOVA
df SS MS F Significance F
Regression 1 0.0019 0.002 0.0511 0.8228
Residual 28 1.0145 0.036
Total 29 1.0164

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.8337 0.8227 1.0134 0.3196 -0.8515 2.5189
X 0.6936 3.0678 0.2261 0.8228 -5.5905 6.9777

a) Write the fitted regression equation

b) State the degrees of freedom for a two-tailed test for zero slope, and use the TINV function to find the critical value at &#945; = .05.

c) Conclusion about slope

d) Interpret the 95% confidence limits for slope

e) Verify that F= square of t

f) Describe the fit of this regression

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