Question 11 The following data provide measurements on the hardness and tensile

Question

Question 11 The following data provide measurements on the hardness and tensile strength of 10 specimens of die-cast aluminum. Use the least squares met determine the coefficients of simple linear regression equation to fit the data given in the table.Assume that we want to use the hardness to predi strength. 29 32 29 78 32 69 fill in the blank by "hardness" or "strength). a The independent variable is: hardness b. The correlation coefficient 0.61952 c. The standard deviations of independent and dependent variables Sx- 22.3914 d. The slope of the regression line b1 2.2222 e The intercept of the regression line bo = 3.3556 f. Given SSR = 267, SSE-428, the coefficient of determination r2-0.3838 (4DP), Sy-21.2424 4DP). (4DP) (4DP)

Explanation / Answer

Ans:

a)hardness

b)r=0.61952

c)sx=3.6742,sy=13.1795

b1=r*sy/sx

d)slope,b1=2.2222

e)intercept,b0=3.3556

f)

R2 = 1 - SSE / SST

R2 =SSR/SST=267/(267+428)=0.3842

hardness,x tensile strength,y 1 29 53 2 32 83 3 29 78 4 23 56 5 32 69 mean= 29 67.8 std dev= 3.6742 13.1795 corr. Coff,r= 0.61952 slope,b1= 2.2222 y-intercept,b0= 3.3556

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