The table below gives the number of hours spent unsupervised each day as well as
ID: 3319496 • Letter: T
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^=b0+b1x , 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 4 of 6 : Determine the value of the dependent variable y^ at x=0 .
Hours Unsupervised 0.5 1 2 2.5 4 5 5.5 Overall Grades 94 87 82 79 70 67 60Explanation / Answer
The statistical softeware output for this problem is:
Simple linear regression results:
Dependent Variable: Overall Grades
Independent Variable: Hours Supervised
Overall Grades = 94.792453 - 6.0754717 Hours Supervised
Sample size: 7
R (correlation coefficient) = -0.98967514
R-sq = 0.97945689
Estimate of error standard deviation: 1.8753616
Parameter estimates:
Analysis of variance table for regression model:
Hence,
Value of dependent variable at x = 0
= y - intercept
= 94.79 [Rounded off to 2 decimal places]
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 94.792453 1.3529148 0 5 70.065351 <0.0001 Slope -6.0754717 0.39349161 0 5 -15.439901 <0.0001Related Questions
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