The linear regression formulas derived in class are m = sigma x_i sigma y_i - n

Question

The linear regression formulas derived in class are m = sigma x_i sigma y_i - n sigma x_i y_i/(sigma x_i)^2 - n sigma s^2_i b = sigma x_i sigma x_i y_i - n sigma x^2_i sigma y_i/(sigma x_i)^2 - n sigma s^2_i (a) Use these formulas to find the line of best fit for the data set {(l, 5.3), (2, 6.5), (3, 8.7), (4, 11.5), (5, 13.2)}. (b) Input the same data into your calculator and use it to find the equation of the regression line. To input data: STAT rightarrow EDIT rightarrow Edit ... and enter data into columns L1 and L2 To get the regression line: STAT rightarrow CALC times 4:LinReg (ax + b) and enter L1 comma L2 rightarrow ENTER (L1 is 2nd 1 and L2 is 2nd 2)

Explanation / Answer

m=(15)*(45.2)-5*156.4/(15)^2-5*55
    =678-782/225-275
    =-104/-50
    =2.08
b=15*156.4-55*45.2/(15)*2-5*55
   =2346-2486/225-275
   =-140/-50
   =2.8
the regression line equation is
Y=mx+b
    =2.08X+2.8

x y xy x2 1 5.3 5.3 1 2 6.5 13 4 3 8.7 26.1 9 4 11.5 46 16 5 13.2 66 25 total 15 45.2 156.4 55

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