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In: Psychology

state %Coll Grad Burglary VehTheft Alabama 19.8 1081.3 288.7 Alaska 28.6 472.1 238.7 Arizona 28 868.9...

state %Coll Grad Burglary VehTheft
Alabama 19.8 1081.3 288.7
Alaska 28.6 472.1 238.7
Arizona 28 868.9 572.6
Arkansas 17.5 1180 228
California 30.6 647.1 523.8
Colorado 35.5 572 273.7
Connecticut 36.8 428.7 256
Delaware 25.6 774.3 291
District of Columbia 46.9 640 1092.4
Florida 25.4 1028.3 346.5
Georgia 27.1 1038.9 409.1
Hawaii 30.4 728.1 398.5
Idaho 25.9 439.8 109.5
Illinois 29.6 612.1 252.5
Indiana 22.6 762.8 273.7
Iowa 24.5 547.9 144.3
Kansas 30.4 699.9 263.9
Kentucky 18.9 675.5 179.6
Louisiana 19.6 982.1 311.6
Maine 24.3 495.4 89.3
Maryland 36.3 689.6 449.7
Massachusetts 36.6 555.5 196
Michigan 24.6 741.5 362.3
Minnesota 34.2 505.9 193.1
Mississippi 21.8 885.6 216.2
Missouri 25 774.5 351.3
Montana 25.4 344.4 162.6
Nebraska 25.4 492 234.8
Nevada 23.4 929 611.6
New Hampshire 32.8 325.7 105.4
New Jersey 36.3 465.3 232.4
New Mexico 27.4 1094.2 403.4
New York 30.4 337.3 128.9
North Carolina 25.3 1210.1 290
North Dakota 27.2 328.3 137.5
Ohio 23 892.8 248.4
Oklahoma 24 963.1 298.7
Oregon 29 550.9 299
Pennsylvania 26 470.9 180.5
Rhode Island 29.2 547.2 304.5
South Carolina 24.2 1026.1 394
South Dakota 25 302.2 99.5
Tennessee 21.5 1046 309.3
Texas 25.5 946 350.8
Utah 29.8 536.5 262.9
Vermont 34.4 557.2 94.2
Virginia 30.6 411.8 170.7
Washington 30.9 801.3 432.6
West Virginia 15.1 609.9 176.6
Wisconsin 25 488.3 204.7
Wyoming 23.4 410 133.9

1) Calculate r for the correlation between percentage of the adult population that graduated from college (Coll Grad) and Burglary rate (Burglary)?

a.

-.20
b.

-.40
c.

-.30
d.

-.10

2) According to your regression output on the previous question, how much variability in the Burglary rate can we predict by knowing the percentage of the population who graduated college?

a. 1%
b.

16%
c.

9%

d. 4%

3) Was this correlation significant?

a. yes

b. no

4) What is r for the correlation between percentage of the adult population that graduated from college (%Coll Grad) and vehicle theft rate (VehTheft)?

a .36

b .42

c .54

d .13

5) According to your regression output on the previous question, how much variability in the vehicle theft rate can we predict by knowing the percentage of the population who graduated college?

a. 13%

b. 16%

c. 22%

d. 36%

6) Was this correlation significant?

a. yes

b. no

7) Now use your regression analysis to predict the burglary rate based on the percentage of college graduates in the area.

What would our predicted Y value be in an area where 20 percent of the population were college graduates?

a. 23074.37
b.

811
c.

1026
d.

612

Solutions

Expert Solution

1.

State X (% Coll Grad) Y (Burglary) X - Mx Y - My (X - Mx)2 (Y - My)2 (X - Mx)(Y - My)
Alabama 19.8 1081.3 -7.586 396.706 57.552 157375.6 -3009.52
Alaska 28.6 472.1 1.214 -212.494 1.473 45153.75 -257.91
Arizona 28 868.9 0.614 184.306 0.377 33968.66 113.113
Arkansas 17.5 1180 -9.886 495.406 97.738 245427 -4897.72
California 30.6 647.1 3.214 -37.494 10.328 1405.809 -120.496
Colorado 35.5 572 8.114 -112.594 65.833 12677.44 -913.558
Connecticut 36.8 428.7 9.414 -255.894 88.618 65481.8 -2408.92
Delaware 25.6 774.3 -1.786 89.706 3.191 8047.145 -160.239
District of Columbia 46.9 640 19.514 -44.594 380.785 1988.635 -870.197
Florida 25.4 1028.3 -1.986 343.706 3.945 118133.7 -682.694
Georgia 27.1 1038.9 -0.286 354.306 0.082 125532.7 -101.429
Hawaii 30.4 728.1 3.014 43.506 9.083 1892.762 131.115
Idaho 25.9 439.8 -1.486 -244.794 2.209 59924.16 363.831
Illinois 29.6 612.1 2.214 -72.494 4.901 5255.397 -160.482
Indiana 22.6 762.8 -4.786 78.206 22.908 6116.16 -374.315
Iowa 24.5 547.9 -2.886 -136.694 8.331 18685.28 394.537
Kansas 30.4 699.9 3.014 15.306 9.083 234.27 46.128
Kentucky 18.9 675.5 -8.486 -9.094 72.017 82.703 77.175
Louisiana 19.6 982.1 -7.786 297.506 60.626 88509.75 -2316.46
Maine 24.3 495.4 -3.086 -189.194 9.525 35794.41 583.905
Maryland 36.3 689.6 8.914 5.006 79.455 25.059 44.621
Massachusetts 36.6 555.5 9.214 -129.094 84.893 16665.29 -1189.44
Michigan 24.6 741.5 -2.786 56.906 7.763 3238.279 -158.555
Minnesota 34.2 505.9 6.814 -178.694 46.427 31931.59 -1217.57
Mississippi 21.8 885.6 -5.586 201.006 31.206 40403.37 -1122.87
Missouri 25 774.5 -2.386 89.906 5.694 8083.068 -214.54
Montana 25.4 344.4 -1.986 -340.194 3.945 115732 675.719
Nebraska 25.4 492 -1.986 -192.594 3.945 37092.49 382.545
Nevada 23.4 929 -3.986 244.406 15.89 59734.24 -974.269
New Hampshire 32.8 325.7 5.414 -358.894 29.308 128805 -1942.95
New Jersey 36.3 465.3 8.914 -219.294 79.455 48089.91 -1954.73
New Mexico 27.4 1094.2 0.014 409.606 0 167777 5.622
New York 30.4 337.3 3.014 -347.294 9.083 120613.2 -1046.65
North Carolina 25.3 1210.1 -2.086 525.506 4.353 276156.4 -1096.35
North Dakota 27.2 328.3 -0.186 -356.294 0.035 126945.5 66.369
Ohio 23 892.8 -4.386 208.206 19.239 43349.69 -913.248
Oklahoma 24 963.1 -3.386 278.506 11.467 77565.53 -943.097
Oregon 29 550.9 1.614 -133.694 2.604 17874.12 -215.746
Pennsylvania 26 470.9 -1.386 -213.694 1.922 45665.18 296.239
Rhode Island 29.2 547.2 1.814 -137.394 3.29 18877.14 -249.195
South Carolina 24.2 1026.1 -3.186 341.506 10.152 116626.3 -1088.13
South Dakota 25 302.2 -2.386 -382.394 5.694 146225.3 912.497
Tennessee 21.5 1046 -5.886 361.406 34.648 130614.2 -2127.33
Texas 25.5 946 -1.886 261.406 3.558 68333.04 -493.083
Utah 29.8 536.5 2.414 -148.094 5.826 21931.87 -357.459
Vermont 34.4 557.2 7.014 -127.394 49.192 16229.26 -893.507
Virginia 30.6 411.8 3.214 -272.794 10.328 74416.63 -876.685
Washington 30.9 801.3 3.514 116.706 12.346 13620.26 410.072
West Virginia 15.1 609.9 -12.286 -74.694 150.953 5579.211 917.712
Wisconsin 25 488.3 -2.386 -196.294 5.694 38531.38 468.412
Wyoming 23.4 410 -3.986 -274.594 15.89 75401.93 1094.608

X Values
? = 1396.7
Mean = 27.386
?(X - Mx)2 = SSx = 1652.86

Y Values
? = 34914.3
Mean = 684.594
?(Y - My)2 = SSy = 3123820.468

X and Y Combined
N = 51
?(X - Mx)(Y - My) = -28365.134

R Calculation
r = ?((X - My)(Y - Mx)) / ?((SSx)(SSy))

r = -28365.134 / ?((1652.86)(3123820.468)) = -0.3948

Therefore, the correct answer is Option B, -.40.

Please post the other questions separately as we are supposed to answer just one question or four subparts of a question.

Hayet Jeridi answered 2 months ago
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