Education reform is one of the most hotly debated subjects on both state and nat

Question

Education reform is one of the most hotly debated subjects on both state and national policy makers list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th-graders. Four explanatory variables are used (1) STR is the student-to-teacher ratio, (2) TSAL is the average teacher's salary, (3) INC is the median household income, and (4) SGL is the percentage of single family households. A portion of the data is shown in the accompanying table (in $1,000) (n $1,000) 11 14 2015 Qc cs. TSAL INC STR% $1,000) (in $1.000) SGL(%) 22700 19.00 44.01 48 89 234.67 14 50 3648 37.56 690 460 238.00 18 10 42.94 57.13 370 230 67 17.90 40.17 4391 233.33 17.50 36 62 44.55 240.00 17.10 47.98 70 76 233 33 1680 45.50 52 75 240.00 17.30 40.56 57 05 6.80 241.00 19.70 42.76 47.35 6 60 4.00 244.33 1680 53 85 65.40 280 23200 17.20 4429 50.39 4.20 3.30 460 228.67 19.70 44 09 4090 6.30 5 80 229,33 18.00 36 40 36.32 640 3.50 225 67 1900 41.50 44.95 460 4.00 22867 1800 4062 4007 730 225.33 20.50 40.51 43.25 236.33 15.60 4480 46 00 227.00 15.50 29.86 49.57 23000 11.40 29.11 32 94 227 67 1760 44.33 40.30 241.67 14.80 43 93 64.54 236 33 1790 35.53 44.00 226.33 1960 42.81 50.68 243.67 17.30 4956 61.05 230.00 1700 40 65 48.04 233 67 19.30 3664 53.30 216.33 27.00 46.48 34.38 233.00 18.70 40 56 38.41 235.00 17.10 47.58 51.92 217.33 19 10 4621 38 54 242.00 15.80 4506 61.80 235.00 1350 47 4460.32 22800 1390 50 45 39.99 233.33 1690 4579 62 47 225 33 1760 42 41 41.99 232 67 12.00 446536.96 237.00 17.2046 9659 37 220.33 2100 41.12 29 04 220.67 17.10 37.38 3556 22967 18.70 44.64 4360 690 230.67 1000 3181 29.39 440 350 227 67 1880 44 93 44 18 450 5 80 223 33 19 50 41.69 5072 3.60 242.33 1700 46 84 6092 3.20 222.00 1980 4521 3721 630 228 33 2100 45.13 44.47 6.80 90 390 23567 1640 3699 48.17 390 226 33 18 10 40.33 4078 660 237 33 19.10 44.34 48.15 4 60 225.00 1570 42.62 4867 410 10.60 238 67 17 80 44 99 5917 390 370 226.33 18.10 43.90 50.10 360 243 67 15 20 39 00 6642 3 10 242 33 1390 41.87 53 21 3.00 3 20 222.67 960 4 5 30 222.33 19 30 4077 3853 5.10 250 226 33 15.10 3668 34.31 940 4.10 23300 16.40 41.32 4596 4.10 13 40 21367 1690 3796 3082 1370 720 240.33 20.00 48 23 5127 3.40 44.75 42.88 310 227.00 18 50 38 8040.14 24467 1570 43.07 74 31 231.33 1690 45 35 51.51 230 33 17.60 34.8839.76 230 33 1660 420752.55 227 33 16.10 36 97 43 40 230 00 17 60 24167 18.00 48.01 68 58 23100 19.3046,5447 46 226 00 15.80 231.00 16.9040.5247.49 420 228.33 19 50 4122 4921 3.80 4.20 22867 15.7042 49 60.18 370 4.50 231 67 16.70 40 87 43 16 3.10 4.60 21933 20 80 43 64 38 53 7.60 430 230 67 1930 46.1256 793.50 4.70 234 332000 3877 52 36 4 227.00199040.94 45 554 00 234 67 16.9042.4851 82 380 23467 18 10 70 Type here to search

Explanation / Answer

The sample linear regression equation is given by,

Score = 227.768 - (0.680*STR) - (0.058 *TSAL) +(0.385*INC) -(0.024*SGL)

So here we can see that the signs of the slope coefficients are negative for STR, TSAL and SGL and it is positive for only INC. So the claim about the signs are correct for STR,INC and SGL but it is not correct for TSAL.

The predicted score value for the first case is = 235.608

The predicted score value for the first case is = 243.308

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