Question

Short Answer Question We have a dataset with n = 10 pairs of observations (6,3), and 1-683, - 813, - 47,405 1.4 56,089, ? - 66,731 What is an approximate 95% confidence interval for the slope of the line of best fit?

Answer 1

Ans :
::SSxx = 47405 -668372. Ang. Given that D= 10 Edi-683 Ed? = 47405 Edidi first we calculate the following , Ey; -813 - 56089 Ex = 66731 1 quantities: 1) SSxx = Ed? - Eli) n 756-1 1o 2) SSyy Egi? - (Edi n ssyy - 56731 - (813) =634-1 lo

3) Ssay Exidi (Edi)l Eyi) n 561.1 Ssmy = 56089 - - 56089 -(683)(813) 10 4 mo> SSxy SSXX 561.1 7561 <♡ 10.7420 ت

5)S2 - MSE = SSE ECHI-8) n-2 n-2 -- Sé SSyy 2 SSyy - (Ssxy) (561.132 SSXX 634.1 756.1 0-2 10-2 7 Sě = 27.2136 8 = 5. 2166 Now we obtain the estimated standard error of fa Se cal VSSxx 5.2166 Sp - V756-1 90-1897 We constouct 95% confidence interval for the slope of the line of best fit Here l-x=0.95 => X = 6.05

- tak, 0-2 Spa, 95.7. confidence tolereal for the slope of the line of best fit + topina Sp) (0.7420-to.o2s,8(0-1897) 0.7420+ to-025,8(0-1897) (0.7420 -(2-3060)(0.1897),0.7420+ (2-3060) (01897)) → 0.3046 , 1.1794) -- 95.3. Confidence intoval for the slope of the line of best fit fo (0.3046 , 1.1794)
Ans : 95% Confidence interval for the slope of the line of best fit is (0.3046 , 1.1794)