Question

Below are some data examining whether reading the textbook for this course is related to class enjoyment.

Time Reading Textbook 1 2 3 4 5 6 1 2 3 5
Class Enjoyment 20 24 35 46 67 80 12 34 34 78
Note: Text Reading Time: 1 = does not read – 6 = only book I have ever read. Class Enjoyment: 1-100 scale.
Calculate the slope
a) 14.50
b) 13.36
c) 19.00
d) 12.43

Answer 1

13.36

Explanation:

I will first create a table

X. Y. XY. X²

1. 20. 20. 1

2. 24. 48. 4

3. 35. 105. 9

4. 46. 184. 16

5. 67. 335. 25

6. 80. 480. 36

1. 12. 12. 1

2. 34. 68. 4

3. 34. 102. 9

5. 78. 430. 25

ΣX = 32

ΣY = 430

ΣXY = 1744

ΣX² = 130

n = 10

The formula for regression line is given as :

Y = a + bX

a = intercept

b = slope

The question requires us to find b which is the slope.

b = nΣXY-ΣXΣY/nΣX²-(ΣX)²

= 10x1744-32x430/10x130-(32)²

= 17440-13760/1300-1024

= 3680/276

= 13.36

b = 13.36