Question

The table below gives the number of hours ten randomly selected students spent studying and their corresponding test grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the test 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 0 1 1.5 2 2.5 3 4 4.5 5 5.5 Grades 64 68 69 70 72 79 80 81 91 96 Table Step 2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

Step 3 of 6:

Find the estimated value of y when x=0x=0. Round your answer to three decimal places.

Step 4 of 6:

Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.

Step 5 of 6:

According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆy^ is given by?

Step 6 of 6:

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

Answer 1

The statistical software output for this problem is :

Step - 1) Slope = 5.452

Step - 2) Y-intercept = 61.191

Step - 3) Estimated value = 61.191

Step - 4) True

Step - 5)  the change in the dependent variable ˆy is = slope = b1

Step - 6) the coefficient of determination = 0.912