Question

1 (50 pts). The following table is a set of data points. X у 2 15 5 12 9 6 12 7 (a) Use table and formulas to find the regression equation. (Note: Cannot use Excel or SPSS to do it.) (b) Estimate the value of y when x = 14.

Answer 1

Answer :-  Given that :-

(X-X) (५ - ५) (x -2)2 (५-१)(x-2) X 2 15 -5 25 - 25 S 12 - 2 2 4 -4 9 06 -५ ५ - 8 2 S 12 07 - 3 25 - 15 X = 28|4:५० (x-7) - 58 (५-१)(x-7) - -52

• X̄ = 28/4

[ X̄ = 7 ]

• ȳ = 40/4

[ ȳ = 10 ]

a)

• b = ∑([X - X̄) (y - ȳ)] /∑(X - X̄)^2

= -52 /58

[ b = -0.89655 ]

• a = ȳ - (b × X̄)

= 10 - (-0.89655 × 7)

= 10 + 6.27585

= 16.27585

[ a = 16.28 ]

• ȳ = a + b.X

[ ȳ = 16.28 + (-0.89655)X

b) Here, X = 14

• ȳ = 16.28 + (-0.89655)X

= 16.28 + (-0.89655 × 14)

= 16.28 - 12.55

[ ȳ = 3.73 ]