A teacher wants to check if there was a linear association between the final grade and the number of absences during the semester. Treating his class of 27 students as a random sample, Minitab returned the following output:

a) What are the null and alternative hypotheses?
b) At 1% significance, is the null rejected?
c) Interpret the coefficient of determination.
d) Find the coefficient of correlation. Interpret.

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Regression Analysis: grade versus absences Analysis of Variance Source Regression absences Error Lack-of-Fit Pure Error Total Model Summary S 6.31164 5.77% Adj ss Adj MS 60.98 60.98 60.98 90.98 25 995.92 39.84 2 143.24 71.62 23 852.67 37.07 26 1056.90 R-sq R-sq (adj) R-sq (pred) 2.00% 0.00% Coefficients DF 1 1 Term Coef SE Coef Constant 75.50 4.07 absences. -1.83 1.48 T-Value 18.57 -1.24 Regression Equation grade = 75.50 1.83 absences F-Value 1.53 1.53 1.93 P-Value 0.227 0.227 P-Value VIF 0.000 0.227 1.00 0.168