Question

The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the 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 Grades
1.5 61
2 64
2.5 70
3.5 71
4.5   74
5 94
5.5 98

Step 1 of 6: Find the estimated slope. Round your answer to three decimal places.

Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6: Determine the value of the dependent variable yˆ at x=0.

Step 4 of 6: Find the estimated value of y when x=2. Round your answer to three decimal places.

Step 5 of 6: Find the error prediction when x=2. Round your answer to three decimal places.

Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

Answer 1

1) From the given data

1) Slope = 8.483

2) Y-Intercept = 46.310

3) If X = 0 then Y = 8.4828(0) + 46.3103 = 46.3103

4) If X = 2 then Y = 8.4828(2) + 46.3103 = 63.2759

5) Prediction Error of X = 2 is 64 - 63.2759 = 0.7241

6) Correlation Coefficient:

Correlation Determination: r2 = 0.91662 = 0.8402