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 = 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
We have a dataset with n = 10 pairs of observations (Xi, Yi), and n Xi...
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...
We have a dataset with n = 10 pairs of observations (Li, Yi), and Xi = 683, Yi = 813, n { x = 47, 405, Xiyi = 56,089, y = 66, 731. i=1 What is an approximate 95% confidence interval for the mean response at 10 = 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% confidence interval for the mean
response at x0 = 90?
We have a dataset with n = 10 pairs of observations (li, Yi), and n n Σ Xi = 683, Yi =...
We have a dataset with n = 10 pairs of observations (li, yi), and n X; = 683, Yi = 813, n _ x* = 47, 405, Xiyi = 56,089, y = 66, 731. i=1 What is an approximate 95% confidence interval for the mean response at Xo = 60?
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?
We have a dataset with n = 10 pairs of observations (Li, Yi), and n X; = 683, Yi = 813, i=1 i=1 2* = 47, 405, XiYi = 56,089, Cy? = 66, 731. i=1 i=1 i=1 What is the coefficient of correlation for this data? We have a dataset with n = 10 pairs of observations (li, Yi), and di = 683, Yi = 813, n x* = 47,405, x:yi = 56,089, y = 66, 731. i=1 i=1 i=1...
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 99% confidence interval for the intercept of
the line of best fit?
We have a dataset with n= 10 pairs of observations (ri, Yi), and n n Σ Xi = 683, 2 yi...
We have a dataset with n= 10 pairs of observations (Li, Yi), and n n Xi = - 683, Yi = 813, i=1 i=1 n n n Στ = 47, 405, Σ tiyi = 56,089, y = 66, 731. i=1 i=1 i=1 What is an approximate 99% confidence interval for the mean response at Xo = 90?
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?
We have a dataset with n = 10 pairs of observations (li, yi), and x = 683, Yi = 813, i=1 n > z* = 47,405, < <iyi = 56,089, Ly} = 66, 731. i=1 i=1 What is an approximate 99% confidence interval for the slope of the line of best fit? We have a dataset with n = 10 pairs of observations (li, Yi), and { x: = 683, yi = 813, i=1 i=1 n r* = 47,405, xiyi...