pop value doct nurse vn deaths 100 141.83 49 76 221 661 110 246.8 103 250 378 11
ID: 3054730 • Letter: P
Question
pop value doct nurse vn deaths 100 141.83 49 76 221 661 110 246.8 103 250 378 1149 130 238.06 76 140 207 1333 142 265.9 95 150 381 1321 202 397.63 162 324 554 2418 213 464.32 194 282 560 2039 246 409.95 130 211 465 2518 280 556.03 205 383 942 3088 304 711.61 222 461 723 1882 316 820.52 304 469 598 2437 328 709.86 267 525 911 2177 330 829.84 245 639 739 2593 337 465.15 221 343 541 2295 379 839.11 330 714 330 2119 434 792.02 420 865 894 4294 434 883.72 384 601 1158 2836 436 939.71 363 530 1219 4637 447 1141.8 511 180 513 3236 1087 2511.53 1193 1792 1922 7768 2305 6774.16 3450 5357 4125 14590 2637 8318.92 3131 4630 4785 19044 (Q-6 in page 460) Data were collected to discern environmental factors affecting health standards. For 21 small regions we have data on the following variables: POP: population (in thousands), VALUE: value of all residential housing, in millions of dollars; this is the proxy for 1. economic conditions, DOCT: the number of doctors, NURSE: the number of nurses, VN: the number of vocational nurses, and DEATHS: number of deaths due to health-related causes(i.e., not accidents); this is the proxy for health standards. The data are given in the following table VN DEATHS 661 1149 110 238.N6 397.63 324 213 11.61 330 89.51 45.15 641 714 2119 1158 1219 136 39 71 447 1141.S0 067 2511.53 SLI 1193 145 352 1792 4125 19044 Perform a regression relating DEATHS to the other variables, excluding POP. Compute the variance-inflation factors; interpret all results. Obviously multicollinearity is a problem for these data. What is the cause of this phenomenon? It has been suggested that all variables should be converted to a per capita basis. Why should this solve the multicollinearity problem? Perform the regression using per capita variables. Compare results with those of part (a). Is it useful to compare R values? Why or why not? a. b. c.Explanation / Answer
We fit a regression model to this data in Minitab:
In Minitab enter the Data the click on "Stat". Select "Regression" . In Response box select deaths colounm and in predictors box select remaining variables. Select "Ok"
The output of the Minitab is as follows:
Regression Analysis: deaths versus value, doct, nurse, vn
The regression equation is
deaths = 530 + 1.30 value + 0.46 doct - 0.880 nurse + 2.14 vn
Predictor Coef SE Coef T P VIF
Constant 530.2 263.6 2.01 0.061
value 1.2958 0.5145 2.52 0.023 56.7
doct 0.464 1.714 0.27 0.790 121.3
nurse -0.8802 0.9071 -0.97 0.346 77.6
vn 2.1423 0.6819 3.14 0.006 31.7
S = 651.033 R-Sq = 98.4% R-Sq(adj) = 98.0%
Analysis of Variance
Source DF SS MS F P
Regression 4 409928560 102482140 241.79 0.000
Residual Error 16 6781508 423844
Total 20 416710068
Source DF Seq SS
value 1 405608308
doct 1 136896
nurse 1 294
vn 1 4183063
Unusual Observations
Obs value deaths Fit SE Fit Residual St Resid
15 792 4294 2905 232 1389 2.28R
18 1142 3236 3187 578 49 0.16 X
20 6774 14590 15030 623 -440 -2.35RX
21 8319 19044 18938 640 106 0.90 X
R denotes an observation with a large standardized residual.
X denotes an observation whose X value gives it large influence.
a. Here, from Analysis of variance table p value is 0.000 which is less than l. o. s. 0.05 also R2 is 0.98 so we can conclude than the model fitting is good for the given data.
Also, VIF for facors value doct nurse vn are 56.7 121.3 77.6 31.7 respectively. Here VIF for all the factors are greater than 10 so it indicates there is multicollinearity is present in the data.
From output we can see than the p value for the predictors value and vn is less than 0.05 so these factors have significant effect on the response death and the p value for factos doct and nurse is greather than 0.05 so these factors are insignificant that is these factors dose not have any effect on response deaths.
b. Here , there is a problem of multicollinearity in the data this may me because of there is a dependencies between the predictors.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.