Problem

Given the data set {(1,3), (2,5), (3,7), (4,9)}, find the regression line.

Answer

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Answer

Step 4: Substitute the computed values of a and b into the regression line equation y=ax+b, we get the regression line as y=1+2x

Steps

Step 1 ：Step 1: Compute the means of x-values and y-values. x¯=1+2+3+44=2.5 and y¯=3+5+7+94=6

Step 2 ：Step 2: Compute the slope (b) of the regression line using the formula b=n(∑xy)−(∑x)(∑y)n(∑x2)−(∑x)2. Substituting the given values, we get b=4(1∗3+2∗5+3∗7+4∗9)−(1+2+3+4)(3+5+7+9)4(12+22+32+42)−(1+2+3+4)2=2

Step 3 ：Step 3: Compute the y-intercept (a) of the regression line using the formula a=y¯−bx¯. Substituting the computed values, we get a=6−2∗2.5=1

Step 4 ：Step 4: Substitute the computed values of a and b into the regression line equation y=ax+b, we get the regression line as y=1+2x

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