Answer:
[tex]b_i = -0.020125[/tex]
Step-by-step explanation:
Given
[tex]\sum x_i= 2000[/tex]
[tex]\sum y_i= 86.6[/tex]
[tex]\sum x_i^2= 216000[/tex]
[tex]\sum x_iy_i = 8338[/tex]
[tex]n = 20[/tex]
Required
Determine the slope (b) of the regression line
This is calculated as:
[tex]b_i = \frac{\sum xy - \frac{\sum x\sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}}[/tex]
Substitute values for each term, we have:
[tex]b_i = \frac{8338 - \frac{2000 * 86.6}{20}}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the numerator
[tex]b_i = \frac{8338 - 8660}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the denominator
[tex]b_i = \frac{8338 - 8660}{216000 - 200000}[/tex]
[tex]b_i = \frac{-322}{16000}[/tex]
[tex]b_i = -0.020125[/tex]