Question

9. The following 11 data pairs relate explanatory variable x, to response variable y 10 14 5 8 9 12 4 7 11 13 6 y 8.04 9.96 5.68 6.95 8.81 10.84 4.26 4.82 8.33 7.58 7.24 y =660.17 (Spoints) such that: X = 9, Y = 7.50, 2xy = 797.6, Xx? =1001, Find : a) equation of linear regression line: Y = A + BX predict the Y if X = 5.5 b) 95% confidence interval for B; is there regression on input variable? c) 90% confidence interval for response if x = 4 90% prediction interval for response if x = 4 Explain difference between these intervals (2points) (4points)

sorry but can you guys use tI-84 calculator to solve the problems

Answer 1

sollt @) If the regression line is, Y = A+Bx is B = $(x;-)(47-) (x-7) = + $ XY-8. tex-72 Â = TT-BX By computing we get, Ê 0-5001 â ã 3-0001 if x=55, y = Â +5.57 = 3.000) + 5.5X0.500) Y = 5.75 (b) 95% confidence interval for B is. - @ + selül tg (0.025) = (0.2334 , 0.7668), (c) If x=4, 98% confidence interval for mean response Corresponding to X=4 is,

where ŷn is the fitted response at 2=4 Hence the 90% Confidence interval will be 90% prediction interval will be, s yn + tp (0-025) [mPe[1+ + -392) a (2.40,7.60). : Difference between the entervals = Confidence Internal : A confidence interval of the prediction is a range that likely contains that mean value of the dependent variable given Specific values of the Prdependent variables. like regular Confidence intervals, these intervals provide a range foo the population avedcinge, Here the resulte shows that we can be 95% confidence that the poput ation defined by (x=4] has a mean that falls within (3.72,6-28). prediction Interval A prediction interval is a dange that likely containg the value of the dependent variable for a single new observation given Specific values of the independent Variables with this type of interval, we are predicting sanges for individuals observationg rather than the mean value. Here we can be 95% conficlent that the trie predicted value of y when x=4] will lie in- Side 2.4,76).