Question

Find the equation of the regression line that relates the variable you chose in question 3 (use this variable as the x-value) to the total weight of discarded garbage (use this variable as the y-value). Write your equation in y = mx + b form, and round your values of m and b to two decimal places.

Answer 1

See Explanation

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:

`\begin{array}{cc}x & {y} & {43} & {99} & {21} & {65} \ \\ {25} & {79} & {42} & {75} \ \end{array}`

Calculate the equation of the regression line.

The equation is calculated using:

`y = mx + b`

Where:

`m = (n(\sum xy ) - (\sum x)(\sum y))/(n(\sum x^2) - (\sum x)^2)`

and

`b = ((\sum y)(\sum x^2) - (\sum x)(\sum xy))/(n(\sum x^2) - (\sum x)^2)`

So, first we fill in the table with columns x^2, y^2 and xy

`\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}`

From the above table.

`\sum x = 43+21+25+42`

`\sum x = 131`

`\sum y = 99+65+79+75`

`\sum y = 318`

`\sum xy = 4257+1365+1975+3150`

`\sum xy = 10747`

`\sum x^2 = 1849 + 441 + 625 + 1764`

`\sum x^2 = 4679`

`\sum y^2 = 9801 + 4225 + 6241 + 5625`

`\sum y^2 = 25892`

`n =4`

Solving for m

`m = (n(\sum xy ) - (\sum x)(\sum y))/(n(\sum x^2) - (\sum x)^2)`

`m = (4 * 10747 - 131*318)/(4*4679 -(131)^2)`

`m = (1330)/(1555)`

`m = 0.86` --- approximated

Solving for b

`b = ((\sum y)(\sum x^2) - (\sum x)(\sum xy))/(n(\sum x^2) - (\sum x)^2)`

`b = (318*4679 - 131*10747)/(4*4679-131^2)`

`b = (80065)/(1555)`

`b = 51.49`

The equation becomes:

`y = mx + b`

`y = 0.86x + 51.49`

Apply the above steps and you will arrive at a solution.