Ʃx = | 683 |
Ʃy = | 813 |
Ʃxy = | 56089 |
Ʃx² = | 47405 |
Ʃy² = | 66731 |
Sample size, n = | 10 |
x̅ = Ʃx/n = 683/10 = | 68.3 |
y̅ = Ʃy/n = 813/10 = | 81.3 |
SSxx = Ʃx² - (Ʃx)²/n = 47405 - (683)²/10 = | 756.1 |
SSyy = Ʃy² - (Ʃy)²/n = 66731 - (813)²/10 = | 634.1 |
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 56089 - (683)(813)/10 = | 561.1 |
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 = 90
ŷ = 30.6147 + (0.7421) * 90 = 97.4035
Critical value, t_c = T.INV.2T(0.01, 8) = 3.3554
99% Prediction interval :
Lower limit = ŷ - tc*se*√(1 + (1/n) + ((x-x̅)²/(SSxx)))
= 97.4035 - 3.3554*5.2167*√(1 + (1/10) + ((90 - 68.3)²/(756.1))) = 74.4287
Upper limit = ŷ + tc*se*√(1 + (1/n) + ((x-x̅)²/(SSxx)))
= 97.4035 + 3.3554*5.2167*√(1 + (1/10) + ((90 - 68.3)²/(756.1))) = 120.3783
30. Short Answer Question We have a dataset with n= 10 pairs of observations ('i, yi),...
Short Answer Question We have a dataset with n = 10 pairs of observations (xi, Yi), and n ri = 683, 683, yi = 813, i=1 i=1 n n r* = 47, 405, riyi = 56,089, y= 66, 731. i=1 i=1 i=1 What is an approximate 99% prediction interval for the response yo at Xo = 60?
Short Answer Question We have a dataset with n = 10 pairs of observations (li, yi), and n n Σ Ti = 683, 813, n 2* = 47, 405, xYi = 56,089, 4? = 66,731. What is an approximate 95% confidence interval for the mean response at xo = 90?
26. Short Answer Question We have a dataset with n= 10 pairs of observations (Li, Yi), and n2 n Ti = 683, yi = 813, i=1 i=1 12 n r* = 47,405, tiyi = 56,089, y = 66, 731. Σ- Σ - i=1 What is an approximate 99% confidence interval for the mean response at Io = 90? 27. Short Answer Question We have a dataset with n = 10 pairs of observations (L'i, yi), and n2 Xi = 683,...
We have a dataset with n= 10 pairs of observations (Li, Yi), and ;ا n n Xi = 683, Yi = 813, i=1 i=1 n n { x = 47, 405, Xiyi = 56,089, vi = 66, 731. i=1 i=1 i=1 What is an approximate 99% prediction interval for the response yo at Xo = = 60?
Short Answer Question We have a dataset with n= 10 pairs of observations (Li, Yi), and n n Σ 683, yi = 813, i=1 i=1 n n n * = 47, 405, Iiyi = 56,089, y = 66, 731. i=1 i=1 i=1 What is an approximate 99% prediction interval for the response yo at Io = 90? What is an approximate 99% confidence interval for the mean response at 20 = 90?
31. Short Answer Question We have a dataset with n = 10 pairs of observations (Ci,y), and n 2 = 683, 813, =1 i1 ** = 47,405, «iyi = 56,089, y² = 66,731. What is an approximate 95% prediction interval for the response yo at :20 = 60?
We have a dataset with n = 10 pairs of observations (xi; yi), and Xn i=1 xi = 683; Xn i=1 yi = 813; Xn i=1 x2i = 47; 405; Xn i=1 xiyi = 56; 089; Xn i=1 y2 i = 66; 731: What is an approximate 95% prediction interval for the response y0 at x0 = 60? We have a dataset with n= 10 pairs of observations (li, Yi), and n n Ii 683, Yi = 813, i=1 п...
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Short Answer Question We have a dataset with n = 10 pairs of observations (li, Yi), and n n Σ Ij = 683, yi = 813, i=1 i=1 n n < 1* = 47, 405, liyi = 56,089, { y = 66,731. i=1 i=1 i=1 What is an approximate 99% confidence interval for the intercept of the line of best fit?
25. Short Answer Question We have a dataset with n= 10 pairs of observations (Li, Yi), and n n r; = 683, Vi = 813, i=1 i=1 12 n n 1 = 47, 405, iyi = 56,089, y = 66, 731. i=1 i=1 What is an approximate 99% confidence interval for the slope of the line of best fit?