HW11Sol1 - STAT 3911 Homework 1 Solutions Instructor Alicia...

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Unformatted text preview: STAT 3911 Homework 1] Solutions Instructor: Alicia Johnson 3.26 3.32 3.38 3.49 Home selling prices: a} (i) y = 9.2 - 7’?.9x= 9.2 *- FT.9(2} — 1b3.2: we would predict that a ltouse with two thousand square feet would sell for $193,299. (ii) y = 9.2 * 2?.9x— 9.2 + FF.9L3J —- 249.2; we would predict that a house with three thousand square feet would sell for $249,299. b] For every increase in house size oi‘one unit [a thousand square feet}, home prices are predicted to increase by 27" ttnits (that is. T? thousand dollars). c} The correlation bwctwcen these two variables is positive. There is a positive slope. Also, bf: putting in different values ot‘x. we can see that as square footage increases. so do predicted home prices. d} The predicted value is 249.2, and the actual value is 399. So the residual isy —,v = 399 249.2 = 59.9. The selling price was 539.899 higher than what would he predicted. e] If a home owner added 599 square i'eet to their existing home. I would increase by 9.5. Theny would increase by ??.9I{9.5J = 38.5.: we would expect its selling price to increase a}- season. How much do seat belts help? aft As seat belt usage (x) increases by l percctttage point, the predicted number oFdeaths per year {y} decreases by 229. Thus the slope is —2?9. h) n) y = 28,919 — aria — easte- 2mm} r 28,919 {it} y = 28,919 — are): —- 28,919 2mm} r spun. out y— 28,919 asex— 28,919 . erotica) = 1,919. NL baseball: a} The slope indicates that for an increase in team batting average of9.199, the predicted team scoring increases by 3.3. c} The r3 is the proportionate reduction in error. An :3 of 9.3? indicates that the prediction error using the regression line to predicty is 32% stnaller than the prediction error using the mean oi'y to predict ,9. NOTE: Another interpretation oi‘r“ is that 32% ot'the variation in}! is accounted for by the linear relationship of}.r with .‘r. Oil and GDP: a] See Rweb output. |Blur scatterplot suggesLs that there is a strong linear relationship between GDP and Oil lConsumption, and that the relationship is positive. b) l-'or,v — annual oil consumption per person (in barrels} and x e gross domestic product (GDP, per person, in thousands of dollars], our least squares regression line is: ,v — -9.l955 - 95464:: c) For every increase in GDP nl" one unit {51999 per person), oil consumption is predicted to increase hf: 9.5464 units [that is. asses barrels per person). dt r3 — 9.2121Ahout229d ot'the variation in}r is accounted for by the linear relationship of _1.' withx. Or we can say that the prediction error using the regression line to predict}! is T2913 smaller than the prediction error using the mean oi}.J to predicty. Mountain bike and suspension type: a} See Rweb output. h} Rweb Output The single regression line does not appear to he the best way to fit the data. I would suggest fitting two separate regression lines: one for bikes with full suspension and one for hi hes with front end suspension. See chh output. For both regression equations. y = price of bike. and x = weight {lbs} Full Suspension: y —- 2432.39 — 44.0% Front End Suspension: _} = 2135.53 — "34.96:: See Rweh output. Yes. using two regression lines seems more reasonable than using one. H" the correlations for full and front end suspension hikes are found separately. 1 would expect that the correlations would be “higher” (closer to “1) for each type ofhike. For front end suspension hikes. the correlation is 43.5388 {sec Rweh output}. and for full suspension hikes. the correlation is 43.952. Thus. the correlations are still negative. but the magnitude of the relationships are far stronger when correlations are examined only among hikes ofa certain suspension type. 3.44] Oil and GDP: Ewes k c:s'1:rip:{file= “f:mpf§on:.5£3§.c5” Rweb:> K s- read.tahlst"!mefRdata.5339.éata'. header=T} Rwdbze atLatth} Rwsb:b nanes:XJ [if “Totion' “GD?” “Oil” Rweh:> Rwehib Ewso:} {it in lm{Di; ~ GDP] Rweb:> sumzarytfitl Call: lmtformula = Oil ~ GDP} Residuals: E1: to Median SQ Max -5.8335 —3.2873 -D.8124 2.0943 T.5269 Coefficients: Estimate Std. Error t value Prt> tll (Intercept: -3.1355 2.5007 —E.O4l H.9E5382 GDP $.5454 0.1033 5.283 C.GCO£5T *‘1 Signif. codes: 0 '***' 9.001 '**' G.U; '*' $.05 ‘ ' fl.l ' ' 1 Residoa; standard error: Editipls R-squared: F-statiscic: Ewe :> plot: 0 + + '. l P", H E (“I 4.451 on 11 degrads of freedom 0.?177. Adjusted R-squared: 0.5921 2T.9? on 1 and 11 3F. p—valus: D.UDDESEQ GDP, Oil. pch=1s, xlah:”GU? in Slcoo's“. ylao=”snnual Consumption {barrelsfpersonj“. main=”oil Consumption vs Rwao:e sbLinetfit} ...
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HW11Sol1 - STAT 3911 Homework 1 Solutions Instructor Alicia...

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