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Performing a Complete Regression Analysis using Given Data

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An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model.
∑X = 40
∑X2 = 200
∑Y = 70
∑Y2 = 545
∑XY = 300

Find the estimated y intercept and slope and write the equation of the least squares regression line. Estimate Y when X is equal to 3 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation and check the relation between coefficient of correlation and coefficient of determination. Finally, perform the test of significance of the slope coefficient.

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THe solution gives detailed steps on performing a complete regression analysis using given data: calculating slope, intercept, regression line, standard error, Mean Square Error, coefficient of determination and coefficient of correlation

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SSx=Σ(x^2)-{(Σx)^2/n}=200-(40^2)/20=120

SSxy=Σxy-{ΣxΣy/n}=300-(40*70)/20=160

Slope=SSxy/SSx=160/120=1.33

Intecept=(Σy/n)-(Σx/n)β1=0.83

So equation of ...

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