Question
Can someone please show me the solutions for a, b, c, and d? thanks.
Listed below are placement test scores for students with their corresponding grade they received in a math course. For the following data use the calculator to create a linear regression model where grade is the response variable and placement test score is the predictor variable. Assign numerical values for the grades as follows: A-1, B-2, C-3, D-4, F-5 Placement Test 80 Score Grade 75 60 80 60 What is the equation of the linear regression model? Round the coefficient values to four decimal places. Using a 0.05 significance level, compare this value with the p-value given by the calculator and determine whether there is a correlation. What is the correlation coefficient? Using your equation for the linear regression model, what grade should one expect with a placement test score of 72? Round to the nearest whole number and then convert this to its corresponding letter grade. a. b. c. d.
Explanation / Answer
a)
Grade ^ = 3 {as b1 = 0}
b)
p-value = 1 , p-value > 0.05
hence we reject the null , there is no correlation
c) r = 0
d)
grade^ = 3
hence C
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SUMMARY OUTPUT Regression Statistics Multiple R 0 R Square 0 Adjusted R Square -0.333333333 Standard Error 1.825741858 Observations 5 ANOVA df SS MS F Significance F Regression 1 0 0 0 1 Residual 3 10 3.333333 Total 4 10 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 3 6.377664398 0.470392 0.670160617 -17.2966 23.29657 -17.2966 23.29657 Placement test -5.41733E-18 0.089087081 -6.1E-17 1 -0.28351 0.283515 -0.28351 0.283515