The table below gives the number of hours ten randomly selected students spent s

Question

The table below gives the number of hours ten randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line., = bo + bix, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Studying 0 0.511.5 2 2.5|3.544.5 6 Midterm Grades 61 68 75798187 90 95 97 99

Explanation / Answer

The regressionequation is

y=b0+b1(x)

from Excel

The fitted regression equation is

y=67.01+6.35(hours studying)

slope=6.35

intercept =67.01

coefficient of determination=0.9210

now  when x=3.5

y=67.01+6.35(hours studying)

y=67.01+6.35(3.5) =89.23

SUMMARY OUTPUT Regression Statistics Multiple R 0.959669 R Square 0.920965 Adjusted R Square 0.911086 Standard Error 3.789539 Observations 10 ANOVA df SS MS F Significance F Regression 1 1338.715 1338.715 93.22133 1.1E-05 Residual 8 114.8849 14.36061 Total 9 1453.6 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 67.01354 2.060726 32.51939 8.72E-10 62.2615 71.76559 62.2615 71.76559 x 6.34763 0.657437 9.655119 1.1E-05 4.831578 7.863682 4.831578 7.863682

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