Find the regression line associated with the set of points. (Round all coefficients to four decimal places.)(5, 7), (7, 11), (11, 15), (13, 3)y(x) = −0.1786x+9.9643 Graph the data and the best-fit line. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
Question
Find the regression line associated with the set of points. (Round all coefficients to four decimal places.)(5, 7), (7, 11), (11, 15), (13, 3)y(x) = −0.1786x+9.9643 Graph the data and the best-fit line. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
Solution
To find the regression line associated with the set of points, we first need to calculate the slope (m) and the y-intercept (b) of the line. The formula for the slope is:
m = [NΣxy - (Σx)(Σy)] / [NΣx^2 - (Σx)^2]
And the formula for the y-intercept is:
b = (Σy - mΣx) / N
Where: N is the number of points, Σxy is the sum of the product of each pair of x,y coordinates, Σx and Σy are the sums of the x and y coordinates respectively, Σx^2 is the sum of the squares of the x coordinates.
Let's calculate these for your points:
N = 4 (since there are 4 points) Σx = 5 + 7 + 11 + 13 = 36 Σy = 7 + 11 + 15 + 3 = 36 Σxy = 57 + 711 + 1115 + 133 = 35 + 77 + 165 + 39 = 316 Σx^2 = 5^2 + 7^2 + 11^2 + 13^2 = 25 + 49 + 121 + 169 = 364
Now we can calculate m and b:
m = [4316 - 3636] / [4*364 - 36^2] = -0.1786 (rounded to four decimal places) b = [36 - (-0.1786)*36] / 4 = 9.9643 (rounded to four decimal places)
So the equation of the regression line is y(x) = -0.1786x + 9.9643
To graph the data and the best-fit line, you would plot the original points and then draw the line y(x) = -0.1786x + 9.9643 through them. Unfortunately, I can't draw a graph for you here, but you can easily do this using graphing software or a graphing calculator.
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