We have a dataset with n = 10 pairs of observations (Xi, Yi), and n Xi...

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Question

We have a dataset with n = 10 pairs of observations (Xi, Yi), and n Xi = 683, Yi = 813, i=1 i=1 n n Cx= 47, 405, Xiyi = 56,08

math Statistics-And-Probability

Answer 1

Answer #1

Sum of Square error, SSE = SSyy -SSxy²/SSxx = 634.1 - (561.1)²/756.1 = 217.70903

Standard error, se = √(SSE/(n-2)) = √(217.70903/(10-2)) = 5.2167

Slope, b = SSxy/SSxx = 561.1/756.1 = 0.7420976

y-intercept, a = y̅ -b* x̅ = 81.3 - (0.7421)*68.3 = 30.614734

Regression equation :

ŷ = 30.6147 + (0.7421) x

Predicted value of y at x = 60

ŷ = 30.6147 + (0.7421) * 60 = 75.1406

Critical value, t_c = T.INV.2T(0.05, 8) = 2.306

95% Confidence interval :

Lower limit = ŷ - tc*se*√((1/n) + ((x-x̅)²/(SSxx)))

= 75.1406 - 2.306*5.2167*√((1/10) + ((60 - 68.3)²/(756.1))) = 69.882

Upper limit = ŷ + tc*se*√((1/n) + ((x-x̅)²/(SSxx)))

= 75.1406 + 2.306*5.2167*√((1/10) + ((60 - 68.3)²/(756.1))) = 80.400

Answer 2

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