Question

The table below gives the number of hours ten 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	0.50.5	11	1.51.5	22	2.52.5	33	44	4.54.5	55	5.55.5
Midterm Grades	6868	7070	7171	7272	7474	7676	7979	8181	8383	9595 Table Copy Data Step 1 of 6: Find the estimated slope. Round your answer to three decimal places. Find the estimated y-intercept. Round your answer to three decimal places. Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false. Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable yˆy^. Determine the value of the dependent variable yˆy^ at x=0x=0. 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:

Simple linear regression results: Dependent Variable: Grades Independent Variable: Hours Grades = 64.227732 + 4.2956841 Hours Sample size: 10 R (correlation coefficient) = 0.92996284 R-sq = 0.86483088 Estimate of error standard deviation: 3.1328849 Parameter estimates: Parameter Estimate Std. Err. Intercept 64.227732 2.0294979 Slope 4.2956841 0.60042739 Alternative DF T-Stat P-value 0 8 31.647105 <0.0001 0 8 7.1543773 <0.0001

Hence,

Step - 1: Slope = 4.296

Step - 2: y - Intercept = 64.228

Step - 3: False

Step - 4: Change independent variable = b1 = 4.296

Step - 5: Value of dependent variable = bo = 64.228

Step - 6: Coefficient of determination = 0.865