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:
[tex]m=\frac{n(\Sigma xy)-\Sigma x\Sigma y}{n(\Sigma x^2)-(\Sigma x)^2}[/tex]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:
[tex]\begin{gathered} m=\frac{11(1991)-110*184.8}{11(1210)-110^2} \\ \\ m=\frac{1573}{1210} \\ \\ m=1.3 \end{gathered}[/tex]The slope of the line is 1.3
To find the y-intercept,b, apply the formula:
[tex]b=\frac{n(\Sigma y^)(\Sigma x^2)-\Sigma x\Sigma xy}{n(\Sigma x^2)-(\Sigma x)^2}[/tex]Plug in the values and solve for b:
[tex]\begin{gathered} b=\frac{(184.8)(1210)-110*1991}{11(1210)-110^2} \\ \\ b=3.8 \end{gathered}[/tex]The y-intercept is 3.8
Therefore, the equation of the regression line is:
y = 3.8 + 1.3x
ANSWER:
[tex]y=3.80+1.30x[/tex]