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# Sp03A_EC41key_upd1 - i—v store EC 41 UCLA Sample...

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Unformatted text preview: i—v store EC 41 UCLA Sample Problems #3; RE Ch 2 material These problems will NOT be collected or graded but they will be useful for studying for exams l) :1) Consider the data on X and Y below. The sample correlation coefﬁcient, r -— t (I (use lixcelt calculator. 01‘ the computation formula‘) 4 I i h) Write the (0118) regression equation on on X: Y = a + bX: Y 7— D l. ? g X X X 2 “error” = residual 2 3 2. 5 , S 2 3 3 '5 i 5 4 3 it; ._ 2 4 S "" 5 0 6 6 n; r: -— 5' 6 '0 “I, £2" 2 t 37 1)) Find Pretlieted Y: when X -- 4 in” =_ g when X =8 l; = f) _ 0) Calculate resizing/{5' for the regression in the previous problem and fill in the above table NOT—F C“ .1“ (D J aiwczrg irptg [he {)L‘E WQFEKEWW 2) Find correlation coefﬁcients and estimated least squares slope coefﬁcients for the four data sets in Table 2.6 on pg. 142. Report: Set A Set B Set C Set D Sample correlations coefﬁcient r -" ‘ 6 . Q h 9 ‘ {8 i :/'V :73 i Estimated slope coefﬁcients b= l I S , r 1 -"I f 0-“ flit-"i iit cant! 3although graph {Ft/955i they are V1767“ riﬂes/yr.“ 3) The sample corre ation coefﬁcient between X and ‘1’ is .3, mean of‘X = 10, mean on = 5. sample standard deviation ofX = 2 and sample standard deviation on = 4. = g » . b 3% r‘ 5 t—g L a) What is the equation ofthe forwar OLS regression on on X? _ - __ l - " \v—r ( ~ ‘i o‘“ s—m-s f w s + I) x b) What is the equation 0 'the reverse OLS regression ot‘X on Y? bf: 535 r r_ L! C5 ) t '25 : g ,7 g + .2 s a: Y ! us. 0) Use the reverse regression to predict the value ofX when Y = 13. Oi : i a. to! \f A x : 37s «MOM 10~ it“: Bit: i7. H ii )4 Height (6 father. son pairs) Y 4) The table to the right shows heights (inches above 5’) for six pairs. > _ _ v __ Observation Father Son :1) Perform the regression of l-tnal score on Midterm score and i 2 3 Write the estimated equation: 2 4 0 Estimated Son‘s Height = a + b(Father’s Height) 3 4 5 4 5 4 .. __ ’3 e- - 5 6 9 ‘ iii.) 4" 6 7 7 Oich r(.b/ LL57 'asl-tl clay LT? 32W b) Perform the reverse regression ofFather's Height on Son‘s Height and write the estimated equation: I Estimated lr'ather's lleight = a‘ + b‘(Son‘s Height ) K’— §gn l!- rx .— 4.5/20d i r" 0 a 6 true :r-u-r i n I . mrlmwdmt darted"? wt“ F'PUHGP ' t \ u ,‘H a . .. | ' . v 11! A X :t "'3‘ {mi ‘1‘ ’3 i C) What is the predicted Son's height ifthe Father's height is 7 (inches above 5') A t . ‘_ h w, “I “ﬁll-{t +1.2 {tie "MM :7) WI ’14”- LXOVS :‘ _ ._________ 3.“; ‘ l- _ q it laud-at {3, . to Fiﬁ! If“? F, a: Ci {dial/f d) What is the predicted Father‘s height ifthe Son‘s height is 9? xi ./ N. . _ _, (1,101,. N “in” 2‘ 3:19 its: ,. -ig/g Fall/1e : t ’3. I 9 7 2(( if. f: 6‘ YE? To Jg"_d______ a , L i ) -i’ A ’ls 1'3“; .q 2, €15 aim}th Irksﬂﬂliir] 6) Write the average heights and the sampie standard deviations for the Son’s and Father’s heights. Fﬁi'llm >1 -. 14.6”! ‘3. i, it: h — l- " to .e X“ I J ,. ))I_](_{ f) What is the standardized z-score ofa Son‘s height of 7 tow many standard deviations is it above the mean?) .. J I i H P _ ’ ‘é-Z ; .74 .t AM .-,-i Lit-"*1 t 39? 34¢; 9st»? ' .4 g) What is the standardized z-seorc ofa Father‘s height of 9 (how many standard deviations is it above the mean?) 0”“‘53 w" [it tum-g; uni-s "67"”? —. ‘7: { '33 ‘1). it "t . .a J 5) it) Which ot'the following is true ofthe least-squares regression ﬁne? A) '1 he slope is the change in the response variable that would be predicted by a unit change in the explanatory variable. B) It always passes through the point (X , Y ), where X and Y are the means ofthe expianatory and response variables. respectively. C 11 will onlzﬁpass through all the data points if r = i l. D All ofthe abde. 3 L “run. run-- .I. b) T m®ihe sum ot'the "residuals" from an ordinary least squares regression are zero only ifthe observations ol'Y are not skewed either upward or downward. e) T 0®Fall data points lie on a straight line. the regression slope b will equal one (or negative one). | . ngril 3x (if Ifthe slope ofan estimated regression line (b) is zero, then the correlation coefﬁcient must also be zero. 6) T or(F“}l"he regression of Y on X assumes that ’ is measured without error. but that X may be measured with error. . i la ; p P WV Lie 0 at“ var/pi?in l l / ‘l i‘ l» r =0 i‘liE/l/ lo. (and is. lit We? .+ L rants-arm Wv‘) haili- tt : o ...
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Sp03A_EC41key_upd1 - i—v store EC 41 UCLA Sample...

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