Question

The table below gives the number of hours five randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1xy^=b0+b1x, for predicting the midterm exam 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	11	22	33	44	55
Midterm Grades	7070	7777	8484	8888	9595

1. Find the estimated slope. Round your answer to three decimal places.

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

3.Find the estimated y-intercept. Round your answer to three decimal places

4.Determine the value of the de[endent variable of ^y at x=0

5.According to the equation of the regression line, if the independent variable is increased by one unit what is the change in the dependent variable y?

6.Not all points predicted by the linear model fall on the same line True or False

7.Substitute the values found in 1 and 2 in to the equation in the regression line to find the linear model.According to this model, if the value of the independent variable is increased by one unit, then find the dependent variable y.

Answer 1

1. The estimated slope is given by = 56.009

2. The coefficient of determination is given by R2 = 0.993

3. The estimated y-intercept is given by = 6514.500

4. We have the estimated regression equation as   = 6514.5 + 56.009x When x = 0, = 6514.500

5. If the independent variable x is increased by one unit, the dependent variable y will increase by units, that is by 56.009 units. In the context of the problem, if a student studies for an extra hour, his midterm grade will increase by approximately 56 units.

6. False. All points predicted by the linear equation will fall on this linear line  = 6514.5 + 56.009x

7. The linear model for this problem is give by   = 6514.5 + 56.009x and the coefficient of determination is R2 = 0.993 Now, if the value of independent variable is increased by one unit, the dependent variable will increase by 56 units, irrespective of the original values of the dependent and independent variables.