In: Statistics and Probability
The table below gives the number of parking tickets received in one semester and the GPA for five randomly selected college students who drive to campus. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the GPA of a college student who drives to campus based on the number of parking tickets they receive in one semester. 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.
Number of Tickets 0 1 2 6 8
GPA 3.1 2.7 2.5 2.3 1.6
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 yˆy^ at x=0x=0.
Step 4 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 5 of 6:
Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Step 6 of 6:
Find the value of the coefficient of determination. Round your answer to three decimal places.
The statistical software output for this problem is :
Step - 1) Slope = -0.152
Step - 2) Y-intercept =2.957
Step - 3) b1
Step - 4) the change in the dependent variable ˆy is = slope = -0.152
Step - 5) True
Step - 6) the coefficient of determination = 0.0.887