Questions 1-17 are related to the following Below are the values for two variables x and y obtained from a sample of size 25. We want to build a regression equation based the sample data. y = bo + bix y X 40.6 8.9 22 5.2 30.2 8.4 23 4.2 20.4 4.9 29.3 7.8 24.3 8.1 28 6.1 49.1 12.3 28.6 7.6 26.5 7.2 41.4 9.5 33.7 13.3 38.4 8.7 25.2 8.4 37.3 10 18.6 4.7 43.6 8.9 35.7 9.4 50.7 12.1 39.4 7.2 47.6 9.2 38.5 7.7 30.8 10.3 34.8 7.5 27.5 7.1 22.7 6.2 32.4 7,7 37.3 9.1 29.4 40.1 8.3 38.4 10.4 18.6 4.8 48.4 9.2 37.6 9.5The sum product of x and y is, 9307.57 9695.39 10099.36 10520.17 The value in the numerator of the formula to compute the slope of the regression equation is, 455.474 174.452 194.221 514.813 3 The sum of squared x is, 2835.23 2726.18 2621.33 2520.51 The slope coefficient by is, 2.9384 3.1147 3.3016 3.4997 5 The intercept coefficient is, 9.8394 9.1106 8.4357 7.8108 6 The predicted value of y for x = 9.4 in the data set is, 45.44 42.46 39.69 37.09 7 The observed y in the data set associated with x = 9.4 is 35.7. The prediction error is, -1.26 -1.39 -1.53 1.68 8 Sum of prediction errors is, 0.00 -0.05 0.50 0.729 Sum of squared errors [SSE] is, a 1399.03 '6 1302.50 c 1221.96 d 1142.02 10 The variance ofthe prediction error is, a 42.3942 '6 39.6212 c 32.0292 d 34.6062 1] On average the observed 5? deviate from the predicted y by. a 6.085 b 5.152 c 4.320 d 3.204 12 Sum of squares total [551'] is. a 3125.281 '6 2926.458 c 2834.222 d 2699.235 13 Sum of squares regression [BBB] is. a 1629.244 '6 1551.661 c 1422.222 d 1402.402 14 The fraction ofvariations in y explained by x is: a 0.5424 '6 0.5950 c 0.6462 d 0.2029 15 The x and y data are sample data from the population ofX and Yto compute 111 as an estimate ofthe population slope parameter 8;. The sample statistic hi is the estimator of the population parameter 31- The estimated measure of dispersion ofthe sample statistic b; is. a 0.2499 '6 0.6520 c 0.5620 d 0.4930 16 The margin of error for a 95% condence interval for [31 is. a 1.0031 11 0.9119 c 0.8290 d 0.?536 1? To perform a hypothesis test with the null hypothesis H\": [31 = 0. we need a test statistic. The test statistic for this hypothesis test is. a 5.5592 11 6.31?3 c ?.1?88 d 815?? Questions lB-Z? are related to the following How much does the size of the living area of a house [x] affect the price of the house [y]? The following data shows the price of the hous B [$1.00 0] and the size [living area in s quare feet]. Use the data below to develop an estimated regression equation that could be us ed to predict the price of the house for a given size. x = Square feet y = Price in thousands of dollars [$1.000] PRICE SQFT 135.4 1161 386.5 3616 91.2 114? 231.9 2389 324.6 2950 339.8 354? 200.5 1918 159 1229 481.1 2855 189.6 1832 160.2 1334 112.2 1651 218.9 2298 136.8 1319 159.? 1?16 215.3 1929 128.4 2805 91.1 1316 490.8 2956 218.2 2454 200.9 3341 1??.1 2899 1?6.8 1365 146.9 154? 113 16?2 113 1672 210.5 2463 110 1433 136.2 1510 204.9 2034 142 2488 88.4 1168 368.8 2543 206.1 2248 199.4 2906 180.5 2811 143.4 1119 145.5 2683 46.6 987 166.8 2121 384.9 5072 88.8 1154 164.7 1593 182.7 2384 198.3 2593 161.3 2801 236.1 2026 162.6 1974 226 2732 231.9 2083 175.1 1115 293.1 3139 101.4 770 146.9 1129 108.4 1318 77.9 1022 212.1 3029 100 753 155.6 1140 110.2 149 114.3 1224 84.5 884 201.6 3154 182.2 1303 352.7 3256 199.3 2112 224.6 3046 152.3 3168 168.3 1367 146.7 1642 116.6 156118 The estimated regression predicts that the price of the house rises by for each additional square foot. 0.07414 $74.14 0.07060 $70.60 0.06724 $67.24 0.06404 $64.04 19 The predicted price for a house with 2,000 square feet of living space is 194.211 $194,211 188.555 $188,555 183.063 $183,063 177.731 $177,731 SSE = 274,808.0 269,419.6 264,136.9 258,957.7 21 SSR = 291,917.3 286,193.4 280,581.8 275,080.2 12 The measure of closeness of fit, or measure of dispersion of observed price around the regression line is, 65.463 $65,463 62.945 $62,945 60.524 $60,524 58.196 $58,196 13 The fraction of variations in house price explained by house size is, 0.6426 0.5950 0.5610 0.5101 24 The house price and size figures above are data from a sample of houses selected from the population of all houses in a geographic area to compute by as an estimate of the population slope parameter B1. The sample statistic by is the estimator of the population parameter B1. The standard error of the sample statistic by is, 0.0053 0.0088 0.0147 0.024525 The margin of error for a 95% confidence interval for the population slope parameter is, 0.01758 $17.58 0.02197 $21.97 0.02747 $27.47 0.03433 $34.33 26 The 95% interval estimate for B, is, 0.0655 0.0827 $65.52 $82.75 0.0618 0.0864 $61.83 $86.44 0.0566 0.0917 $56.56 $91.71 0.0490 0.0992 $49.02 $99.25 27 The value of the test statistic to test the hypothesis that house size has no impact on house price is, 11.2008 10.1825 9.2568 8.4153 Questions 28-35 are related to the following The following table is the regression summary output for a model depicting the impact household weekly income (INCOME in $100) on household weekly expenditure on food (FOOD DEPENDENT VARIABLE = FOOD Regression Statistics Multiple R 0.5043 R Square a = 0.05 Adjusted R Square 0.2433 t_a/2,df = 1.995 Standard Error Observations 70 ANOVA df SS MS F Stat P-value Regression 452687.2 23.189 0.00001 Error 19521.79 Total 69 1780169 bi se(b_j) Stat P-value Lower 95%Upper 95% Intercept 60.8303 1.9423 0.05624 -3.2324 239.5377 INCOME 0.00001x = INCOME Hundreds of dollars [$100] y= Foon Dollars [$1 Use the following calculations rst: Exy = 866868.2 = 20 _ = 29.29114 = 399.825 28 The model predicts that weekly expenditure on food rises by _ for each additional $100 weekly income. a $10.58 '6 $9.62 c $8.24 d $2.95 29 The predicted weekly expenditure on food for a household with $1500 weekly income is. a $262.40 '6 $252.30 c $242.60 d $233.22 30 SSE : a 1381.112 '6 1354.031 c 1.322.481 d 1301.452 31 The measure of closeness oft. or measure of dispersion of observed expenditure on food around the regression line is, a $152.68 '6 $148.23 c $143.91 d $139.22 32 The fraction ofvariations in food expenditure explained by weekly income is, a 0.3022 '6 0.2292 c 0.2543 d 0.2312 33 se[b1] = a 1.4922 '6 1.9920 c 2.6626 d 3.5501 34- The test statistic to test the hypothesis that weekly income has no impact on food expenditure is. a 2.466 1:- 3.682 c 3.852 :1 $815 35 The 95% interval estimate for the population slope parameter is. a 5.631 13.601 1:- 6.868 12.364 c ?.'?21 11.512 :1 8.309 10.923