Is performance on the first exam predictive of performance on the second exam? I

Question

Is performance on the first exam predictive of performance on the second exam? In order to answer this question, a teacher "randomly" selected 70 students and looked at their scores on the first and second exams. X bar = 83.224 S_xx = 10007.758 a. Find and interpret the linear correlation coefficient. b. Find and interpret the coefficient of determination. c. Find the estimated regression line: interpret the slope. d. For what values of exam 1 scores can this model be used to predict exam 2 scores? e. Test to see if there is a linear relationship between exam 1 score and exam 2 score. f. Create and interpret a 90% confidence interval for the slope of the simple linear regression model.

Explanation / Answer

a) the linear coefficient r is sqrt(0.4057) = 0.6369 , which means that the variables Exam1 and Exam2 are moderately correlated in the positive direction

b) The r sqaure value is 0.4057 , which means that the regression equation is able to capture 40.57% variation of the data

c) The regression line is formed using the coefficients as

Exam2 = Exam1*0.7531 + 8.5013

d)

From the scatterplot , we see that the Exam1 scores range from 40 to 100 , hence the model is trained only on this range of exam1 values , hence we can use the values in the range 40-100 to predict the values of exam2

e)

From the anova table , we see that the p value is

3.076e-09 , which is very less than 0.05 , hence the model is statistically significant and there is a linear relationship between the 2 variables

Please note that we can answer only 4 subparts of a question at a time , i have answered 5 .

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