Question

A math professor is interested in the relationship between students' performance on the first midterm in his class and their performance on the second midterm in his class. He gathers the midterm 1 and midterm 2 data for his n = 112 students. This data is called "Midterm 1" and "Midterm2" respectively in the scores.R data file. Note that the scores for both midterm 1 and midterm 2 are out of 100 points. a. Create a scatterplot of the data. Describe the general relationship (trend) of the midterm 1 and midterm 2 scores. b. What is the correlation between midterm 1 grades and midterm 2 grades? Interpret this correlation. c. State the least-squares estimate of the model predicting midterm 2 scores from midterm 1 scores. d. Interpret the slope of this regression equation in the context of the data. e. Predict the midterm 2 score of a student who scored 60 on midterm 1.

Midterm1 = (83.33, 98.33, 75, 91.67, 96.67, 95, 86.67, 65, 100, 100, 80, 88.33,
96.67, 96.67, 90, 96.67, 86.67, 93.33, 80, 91.67, 98.33, 86.67, 85, 86.67, 95,
83.33, 96.67, 81.67, 98.33, 100, 95, 93.33, 91.67, 88.33, 98.33, 93.33, 98.33,
93.33, 85, 88.33, 100, 98.33, 96.67, 90, 86.67, 100, 96.67, 98.33, 90, 96.67,
86.67, 95, 78.33, 86.67, 100, 81.67, 96.67, 91.67, 96.67, 96.67, 95, 96.67, 73.33,
100, 93.33, 96.67, 88.33, 70, 96.67, 96.67, 100, 88.33, 96.67, 100, 88.33, 100,
78.33, 93.33, 96.67, 71.67, 88.33, 71.67, 96.67, 93.33, 96.67, 95, 98.33, 78.33,
90, 96.67, 71.67, 95, 83.33, 90, 96.67, 83.33, 100, 83.33, 78.33, 93.33, 81.67,
93.33, 91.67, 93.33, 75, 70, 85, 70, 91.67, 93.33, 95, 95)

Midterm2 = (80, 96, 70, 87, 93, 81, 96, 85, 100, 86, 65, 80, 93, 89, 100, 100,
80, 98, 55, 93, 69, 85, 67, 84, 90, 89, 80, 80, 80, 92, 80, 86, 88, 79, 96, 90,
98, 93, 82, 97, 100, 96, 74, 85, 96, 90, 94, 96, 94, 88, 92, 85, 62, 71, 97, 76,
79, 100, 84, 100, 94, 98, 78, 90, 86, 83, 94, 45, 86, 64, 92, 94, 100, 100, 82,
91, 62, 92, 92, 89, 94, 64, 80, 96, 78, 97, 78, 87, 72, 91, 81, 92, 76, 76, 100,
73, 100, 91, 96, 96, 75, 100, 90, 85, 76, 85, 84, 72, 81, 90, 70, 96)

Answer 1

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I use R software for calculations.

(d) Here slope = B1 = 0.662. The estimate is 0.662, means that for every 1 unit increase in Midterm 1 score, we expect a 0.662 point increase in the Midterm 2 score. (e) newdata-data.frame (Midterm1=60) predict(model,newdata, interval = "predict") ## fit lwr upr ## 1 65.80251 45.6977 85.90732 The predicted Midterm 2 score = 65.80251