B.predict the final course l. Table 1 Useful statistics for correlation between

Question

B.predict the final course l. Table 1 Useful statistics for correlation between midterm grade and grade course Input-Average of Midterm Exams output Final Course Grade 11.2 13.2 Correlation coefficient- 0.88 A professor believes there is a strong correlation between a student's average on their midterm exams and their final course grade, so she used the data from her statistics class to test her hypothesis. The data she accumulated is shown in Table 1. a. Based on the information above, find an equation of the least squares regression b. Predict the final course grade for a student who has a midterm exam average of 88.2

Explanation / Answer

we know that the equation of the simple regression line is given as

PREDICTED Y = a + b X , where b is beta and a is intercept

Now using the formula beta = r*Sy/Sx ,

putting the values we get beta as

0.88*11.2/13.2 = 0.744

now a = ybar - beta*xbar

= 80-77.7*0.744 = 22.19

so the equation becomes Y = 22.19 +0.744*X

now put x = 88.2 in this equation

Y = 22.19 +0.744*88.2 = 87.81

hope this helps !!

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