Final answer:
The equation for the least squares line is ŷ = -173.51 + 4.83x, and the correlation coefficient (r) is approximately 0.663.
Step-by-step explanation:
To find the equation for the least squares line, we can use the formula:
ŷ = bx + a
where b is the slope of the line and a is the y-intercept.
From the given information, we have n = 8, x = 40, y = 48, xy = 240, x2 = 210, and y2 = 288.
Using these values, we can calculate the slope:
b = (n * xy - x * y) / (n * x2 - x^2)
= (8 * 240 - 40 * 48) / (8 * 210 - 40^2)
≈ 4.83
We can then calculate the y-intercept:
a = (y - b * x) / n = (48 - 4.83 * 40) / 8
≈ -173.51
So the equation for the least squares line is ŷ = -173.51 + 4.83x.
The correlation coefficient (r) can be found using the formula:
r = √((n * Σxy - Σx * Σy) / (sqrt(n * Σx^2 - (Σx)^2) * sqrt(n * Σy^2 - (Σy)^2)))
Substituting the given values, we get:
r = √((8 * 240 - 40 * 48) / (sqrt(8 * 210 - (40^2)) * sqrt(8 * 288 - (48^2))))
≈ 0.663
Therefore, the correlation coefficient (r) is approximately 0.663.