The following data shows the hours studied (X) and marks obtained (Y)

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Module 2: Statistical Decision Theory and Bayesian Learning

20267m

The following data shows the hours studied (X) and marks obtained (Y) by 6 students: X = 2, 3, 5, 6, 8, 9; Y = 50, 55, 65, 70, 80, 85. Find the regression equation of Y on X and predict the marks for a student who studies 7 hours.

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Regression of marks on study hours

Data: (X=(2,3,5,6,8,9)), (Y=(50,55,65,70,80,85)). The points lie exactly on a straight line: every additional study hour corresponds to 5 additional marks.

The least-squares line is (\hat Y=a+bX), with slope (b=S_{xy}/S_{xx}=5) and intercept (a=\bar Y-b\bar X=40).

Regression equation: (\boxed{\hat Y=40+5X})

For (X=7): (\hat Y=40+5(7)=\boxed{75}) marks.

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