Question

(1 point) For the data set (-2,-2), (2, 2), (4,5), (9,8), (9, 12), find interval estimates (at a 95.6% significance level) for single values and for the mean value of y corresponding to x = 2. Note: For each part below, your answer should use interval notation. Interval Estimate for Single Value = Interval Estimate for Mean Value =

Answer 1

Solution Given data set goe d (-2,-), (41),(4,5),(9,8), Carin) Xq-Y 42 108 25 18.6 total = 22 The sum of squares Sexe = & X² - 1 2 ( x ) = 186- + (22) = 89.2 3 Syyat can cus) = 2411 (25) - 116 Ssxy = {4, - - m ( x ) (4) = 208 -(02) 625) = 98

- Coefficients are The slope and to enter cept B = 55xy ssxx 98 89.4 1.0987 Bo= 7-8, X E5-1.0987x4.4 = 0.1659 .. The regression equation in ý = 0.1659 +10987x for single values and for the mean value of y corresponding to u22 = 0.1659 + 1.098782 22.3632 The total Sumo Squares is Sstoral SSyy 5116 regression som of squares Ssrgronion = ß, SS24 The - 1.0987 x 98 = 107.6682

- We know that Sstotal = 55 regression tsserror SSerror = S Staten - Ssregression . P = 116-107.6662. 8-3318 - Hence, the meand sequared error is MSE = Sterror hol %.331% . 5-2 2.7773 error How, taking square root, we get the standard of the estimate F = IMSE 2.7773 - 1-6665 The margin of error of Prediction inte

= 3.352 2.1773/1+5+ (2-4.912) - 89.2 - 6.05 interval estimate for Single value (at a as.6% significance level) a=2 = 19- E, ĝ+E). = (2-3632 - 6.05 , 2.3632+605) interval estimate =/(-3.6860, 8.4132) for Single value the The of error of confidence margin and intural Eakatione fact that 33352x] 2.2173( 3 4 kematian 2.8732

(5) Intuval estimate for mean value (at 95.6% Singnificance level) a = 2 - (ŷ-E, ģ'+E) - (2.3632 - 2.8732, 2.3632+28 732) intuval = 160.5099, 5.5364) estimate for ment value i interveed Estimate for Single value =(-3.6060, 2.41323 Internal Entimate for Mean value = (-0.5099, 5.53645)