1.4) A Simple Example of Regression Analysis s look at a fairly simple example o

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1.4) A Simple Example of Regression Analysis s look at a fairly simple example of regression analysis. Suppose you've accepted a summer job as a weight guesser at the local amusement park Magic Hill. Customers pay two dollars each, which you get to keep if you guess their weight within 10 pounds. If you miss by more than 10 pounds then you have to return the two dollars and give the customer a small prize that you buy from Magic Hill for three dollars each. Luckily, the friendly managers of Magic Hill have arranged a number of marks on the wall behind the customer so that you are capable of measuring the customer's height accu- rately. Unfortunately, there is a five-foot wall between you and the customer, so you can tell little about the person except for height and (usually) gender On your first day on the job, you do so poorly that you work all day and somehow manage to lose two dollars, so on the second day you decide to collect data to run a regression to estimate the relationship between weight and height. Since most of the participants are male, you decide to limit your sample to males. You hypothesize the following theoretical relationship: where: Yi the weight (in pounds) of the ith customer Xi = the height (in inches above 5 feet) of the ith customer fi = the value of the stochastic error term for the ith customer this case, the sign of the theoretical relationship between height and weight is believed to be positive (signified by the positive sign above X, in the general theoretical equation), but you must quantify that relationship in order to estimate weights given heights. To do this, you need to collec set, and you need to apply regression analysis to the data. t a data The next day you collect the data summarized in Table 1.1 and run your regression on the Magi c Hill computer, obtaining the following estimates: Po=103.40 1=6.38 This means that the equation Estimated weight= 103.40+6.38-Height(inches above five feet) (1.21)

Explanation / Answer

Please find excel sheet below:-

a) The coefficients are different because the two data sets used for building the 2 models are different. The average height of 2nd batch was much more while the variance was lesser than in 1st batch. b) Equation 1.21 has the steeper relationship between weight and height, while the second equation (1.24) has the higher intercept.
The two equations intersect at: X = 9.234043 c) =125.1 + 4.03*H39 =IF(ABS(J39-I39)<=10,1,0) 9.234042553 No. H W Equation prediction Accurate Error Original error absolute errors abosulte original errors 1 5 140 145.25 1 5.25 -140 5.25 140 2 9 157 161.37 1 4.37 -157 4.37 157 3 13 205 177.49 0 -28 -205 27.51 205 4 12 198 173.46 0 -25 -198 24.54 198 5 10 162 165.4 1 3.4 -162 3.4 162 6 11 174 169.43 1 -4.6 -174 4.57 174 7 8 150 157.34 1 7.34 -150 7.34 150 8 9 165 161.37 1 -3.6 -165 3.63 165 9 10 170 165.4 1 -4.6 -170 4.6 170 10 12 180 173.46 1 -6.5 -180 6.54 180 11 11 170 169.43 1 -0.6 -170 0.57 170 12 9 162 161.37 1 -0.6 -162 0.63 162 13 10 165 165.4 1 0.4 -165 0.4 165 14 12 180 173.46 1 -6.5 -180 6.54 180 15 8 160 157.34 1 -2.7 -160 2.66 160 16 9 155 161.37 1 6.37 -155 6.37 155 17 10 165 165.4 1 0.4 -165 0.4 165 18 15 190 185.55 1 -4.4 -190 4.45 190 19 13 185 177.49 1 -7.5 -185 7.51 185 20 11 155 169.43 0 14.4 -155 14.43 155 -52 -3388 135.71 3388 Answer: 17 out of 20 are correct Absolute errors and normal errors are BOTH HIGHER for equation #2
Hence, we should go for equation 1 as it has LOWER errors. (SAME accuracy)

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