The table below gives the number of hours spent unsupervised each day as well as

Question

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, cap y = b_0 + b_1 x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. 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. Step 5 of 6: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model if the value of the independent variable is increased by one unit, then find the change in the dependent variable bar y.

Explanation / Answer

The Regression equation is

y=a+bx

From Excel

The fitted Regression eq is

y hat=100.47 -10.02 (Hours)

Hence if we change one unit in independent variable then there is 10.02 units decreased in dependent variable

SUMMARY OUTPUT Regression Statistics Multiple R 0.939002 R Square 0.881726 Adjusted R Square 0.858071 Standard Error 5.616233 Observations 7 ANOVA df SS MS F Significance F Regression 1 1175.718 1175.718 37.2746 0.001708 Residual 5 157.7104 31.54207 Total 6 1333.429 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 100.4756 4.723372 21.27201 4.26E-06 88.33379 112.6174 88.33379 112.6174 Hours -10.0183 1.640919 -6.10529 0.001708 -14.2364 -5.80018 -14.2364 -5.80018

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