Question

Homework: Go - GradedWeek 7 Homework=HW Score: 61.44%, 13.52of 22 pointsQuestion 16, 10.2.9Part 1 of 3O Points: 0 of 1SaveUse the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by theregression line.X1112138106715 5y 19.35 20.24 20.84 15.04 18.20 10.76 13.04 21.2114 921.16 16.758.21ŷ=+x (Round to two decimal places as needed.)Help me solve this View an exampleGet more help.Clear allCheck answePLDNOORICAacerHD-1080-

Answer 1

From the table, we have the points:

(x, y) ==> (11, 19.35), (12, 20.24), (13, 20.84), (8, 15.04), (10, 18.20), (6, 10.76), (7, 13.04), (15, 21.21), (5, 8.21), (14, 21.16), (9, 16.75)

Let's find the regression line.

Apply the slope-intercept form:

y = b + mx

Where:

b is the y-intercept and m is the slope.

To find the slope, apply the formula:

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

Where:

n is the number of data = 11

∑x = 5 + 6 + 7 + 8 + 9 + 1 0+ 11 + 12 + 13 + 14 + 15 = 110

∑y = 8.21 + 10.76 + 13.04 + 15.04 + 16.75 + 18.2 + 19.35 + 20.24 + 20.84 + 21.16 + 21.21 = 184.8

∑xy = 5⋅8.21 + 6⋅10.76 + 7⋅13.04 + 8⋅15.04 + 9⋅16.75 + 10⋅18.2 + 11⋅19.35 + 12⋅20.24 + 13⋅20.84 + 14⋅21.16+15⋅21.21 = 1991

∑x² = 5² + 6² + 7² + 8² + 9² + 10²+ 11² + 12² + 13² + 14² + 15² = 1210

Now, plug in the values into the formula and solve for the slope, m:

`\begin{gathered} m=(11(1991)-110*184.8)/(11(1210)-110^2) \\ \\ m=(1573)/(1210) \\ \\ m=1.3 \end{gathered}`

The slope of the line is 1.3

To find the y-intercept,b, apply the formula:

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

Plug in the values and solve for b:

`\begin{gathered} b=((184.8)(1210)-110*1991)/(11(1210)-110^2) \\ \\ b=3.8 \end{gathered}`

The y-intercept is 3.8

Therefore, the equation of the regression line is:

y = 3.8 + 1.3x

ANSWER:

`y=3.80+1.30x`