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Given the information, find the equation for the least squares line as well as the correlation coefficient. n = 8, x = 40, y = 48, xy = 240, x2 = 210, y2 = 288 y'= r=

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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.

User Occasl
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