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, y-bo + by 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. Hours unsupervised-5-1.5-3-5145 Overall Grades 97 96 | 88 | 83 70 | 63 Table Copy Data Step 3 of 6: Find the estimated value of y when x 3. Round your answer to three decimal places Answer(-How to Enter) 2 Points Keypad

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Overall Grades
Independent Variable: Hours Supervised
Overall Grades = 102.88728 - 8.8612717 Hours Supervised
Sample size: 7
R (correlation coefficient) = -0.99100675
R-sq = 0.98209438
Estimate of error standard deviation: 1.8809972

Parameter estimates:

Analysis of variance table for regression model:

Since p - value is almost 0, we can say that the correlation is statistically significant.

Hence,

For x = 3:

y = 102.88728 - 8.8612717 (3)

y = 76.303

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 102.88728 1.4478615 0 5 71.061551 <0.0001 Slope -8.8612717 0.5350928 0 5 -16.560252 <0.0001

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