Answer:
See Explanation
Step-by-step explanation:
The question has missing details as no link is provided to the "question 3".
However, I'll give a worked solution on how to calculate the equation of a regression line.
Using the following data:
[tex]\begin{array}{cc}x & {y} & {43} & {99} & {21} & {65} \ \\ {25} & {79} & {42} & {75} \ \end{array}[/tex]
Calculate the equation of the regression line.
The equation is calculated using:
[tex]y = mx + b[/tex]
Where:
[tex]m = \frac{n(\sum xy ) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}[/tex]
and
[tex]b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}[/tex]
So, first we fill in the table with columns x^2, y^2 and xy
[tex]\begin{array}{ccccc}x & {y} & {xy} & {x^2} & {y^2 }& {43} & {99} & {4257} & {1849} & {9801} & {21} & {65} &{1365} &{441} & {4225}\ \\ {25} & {79} & {1975} & {625} & {6241}& {42} & {75} &{3150} & {1764} & {5625}\ \end{array}[/tex]
From the above table.
[tex]\sum x = 43+21+25+42[/tex]
[tex]\sum x = 131[/tex]
[tex]\sum y = 99+65+79+75[/tex]
[tex]\sum y = 318[/tex]
[tex]\sum xy = 4257+1365+1975+3150[/tex]
[tex]\sum xy = 10747[/tex]
[tex]\sum x^2 = 1849 + 441 + 625 + 1764[/tex]
[tex]\sum x^2 = 4679[/tex]
[tex]\sum y^2 = 9801 + 4225 + 6241 + 5625[/tex]
[tex]\sum y^2 = 25892[/tex]
[tex]n =4[/tex]
Solving for m
[tex]m = \frac{n(\sum xy ) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}[/tex]
[tex]m = \frac{4 * 10747 - 131*318}{4*4679 -(131)^2}[/tex]
[tex]m = \frac{1330}{1555}[/tex]
[tex]m = 0.86[/tex] --- approximated
Solving for b
[tex]b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}[/tex]
[tex]b = \frac{318*4679 - 131*10747}{4*4679-131^2}[/tex]
[tex]b = \frac{80065}{1555}[/tex]
[tex]b = 51.49[/tex]
The equation becomes:
[tex]y = mx + b[/tex]
[tex]y = 0.86x + 51.49[/tex]
Apply the above steps and you will arrive at a solution.
