1) Very briefly, but precisely, interpret the estimated correlation coefficient
ID: 3363512 • Letter: 1
Question
1) Very briefly, but precisely, interpret the estimated correlation coefficient (tell me the direction of the correlation and the strength of the correlation).
1) List (and label) the dependent variable and the independent variable.
2) Based on the regression results, if a county’s percent of the population with at least a high school diploma increases by 1, by how much and in what direction does a county’s Median Income change?
3) What is the predicted MedInc for a HSDegree of 70 percent?
4) What proportion of the variation in MedInc is explained by our regression model (explained by variation in HSDegree)?
on table Medlnc HSDegr BaDegr FemHea years 3 Count 4 Barbour County 5 Berkeley County 55,100 66.1 20.3 Medlnc($) HSDegree-0.033 Boone County 42,740 7 Braton County 8 Brooke County 9 Cabell County 10 Calhoun County 31,017 66.9 17.641.6 12.5 44.0 44.067 18.6 46.3 11.2 42.7 32,933 12 Doddridge County40,329 63.212.7 13 Fayette County 21.0 42.8 12.537.9 35,625 41,600 15 Grant County 16 Greenbrier County 40,256 66.018.2 17 Hampshire County 26,828 67.5 18 Hancock County39,342 70.216.8 16.5 45.2 18.4 43.8 16.8 45.3 on questions go in this 36,465 20 Harrison County43,13066.920.2 21 Jackson County40,733 68.016.2 22 Jefferson County 66,20559.8 28.3 23Kanawha County46,583 62.7 24.320.6 42.5 16.6 42.3 15.439.4 38,006 35,623 16.6 43.8 16.2 41.8 17.842.3 25 Lincoln County 26 Logan County 27 Marion 23,60758.7 43,085 41.978 73.0 15.9 28 Marshall County 17.941.3 30 McDowell County 38,297 31 Mercer County35,678 32 MinerCounty 30,713 0.1 42.7 19.042.3 19.042.7 17.941.4 15.429.9 73.3 34 Monongalia Count 46,166 52.438.8 35 Monroe County38,233 36 Morgan County 37.406 65.616.5 37 Nicholas County 38,75570.213.6 38 Ohio County 39 Pendleton County 36,052 67.014.0 40 Pleasants County 43,831 41 Pocahontas Coun 34,761 42 PrestonCounty 45,806 69.8 12.9 43 Putnam County55,93966.6 23.3 44 Raleigh County 45 Randolph County40,14665.0 46 Ritchie County 12.4 44.0 40,342 12.5 43.4 11.3 42.3 14.2 41.3 17.940.9 41,152 39.118 16.2 43.6 48 Summers County 49 Taylor County 50 Tucker County 35,04068.113.0 39.933 38,663 39.974 39,188 19.642.5 8.3 47.3 13.441.3 19.742.6 52 Upshur County 53 Wayne County 54 Webster County 28,30762.6 55 Wetzel County 56 Wirt County 57 Wood County 58 Wyoming Count 38,066 16.7 45.5 16.2 42.3 34,620 61 Medlnc Median income of families in the county for the prior 12 months (adusted for inflation)Explanation / Answer
Solution- A. Correlation cofficient is equal to 0.0332
This implies the strength of linear relationship between the two variables. As it is a very low value then this suggests presence of very weak or no linear relationship possible between the given two variables.
Dependent variable is median income and independent variable is HSdegree
B. Regression equation is -
Median income = 42273.35 - 49.414 * HSDegree
When HSdegree increases by 1, then median income falls by 49.414 units
C.When HSdegree equals 70 , then median income is 42273.35 -49.414 *70 units
= 38814.37
D.Value of cofficient of determination = R2 = 0.001099
This is the proportion of the variation in MedInc is explained by our regression model.
Answers
TY!
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