My Notes Ask Your The invasive diatom species Didymosphenia geminata has the pot
ID: 3365363 • Letter: M
Question
My Notes Ask Your The invasive diatom species Didymosphenia geminata has the potential to inflict substantial ecological and economic damage in rivers. An article described an investigation of colonization behavior. One aspect of particular interest was whether -colony density was related torock surface area. The article contained a scatterplot and summary of a regression analysis. Here is representative data 50 71 55 50 33 58 79 26 V 161 1938 57 31 11 14 44 16 69 44 37 70 20 45 49 y 278 47 180 22 52 194 34 (a) Fit the simple linear regression model to this data. (Round your numerical values to three decimal places.) Predict colony density when surface area 70 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density corresponding residua Predict colony density when surface area 71 and calculate the corresponding residual. (Round your answers to the nearest whole number.) colony density corresponding residual How do the residuals compare? O The residuals for both points are negative O The residuals for both points are positive. O The residual for the first point is positive, while the residual for the second point is negative O The residual for the first point is negative, while the residual for the second point is positive (b) Calculate the coefficient of determination. (Round your answer to three decimal places.)Explanation / Answer
Regression Equation is
Y = bX + a
b = (NXY - (X)(Y)) / (NX2 - (X)2)
a = Mean of Y – b* Mean of X
Sr. No.
x
y
x*y
x^2
1
50
161
8050
2500
2
71
1938
137598
5041
3
55
57
3135
3025
4
50
31
1550
2500
5
33
11
363
1089
6
58
14
812
3364
7
79
44
3476
6241
8
26
16
416
676
9
69
278
19182
4761
10
44
47
2068
1936
11
37
180
6660
1369
12
70
22
1540
4900
13
20
52
1040
400
14
45
194
8730
2025
15
49
34
1666
2401
Sum
756
3079
196286
42228
Average
50.4
205.2667
b = (15*196286 – 756*3079) / (15*42228 – (756^2))
= 9.963254
a = 205.2667 – 9.963254*50.4
= - 296.881
Answer A
Y = 9.963254*X – 296.881.
For Surface Area 70
Colony Density y(cap) = 9.963254*70 – 296.881
= 400.546.
Corresponding Residual is given by Y - Y(cap)= 22 – 400.546
= -378.546.
For Surface Area 71
Colony Density Y(cap)= 9.963254*71 – 296.881
= 410.5097.
Corresponding Residual is given by Y - Y(cap)= 1938 – 400.546
= 1527.49.
The Residual for the first point is negative and the residual for the second point is positive.
Answer B
Sr. No.
x
y
x*y
x^2
Y(cap)
(Y(cap)-Y(mean))^2
(Y-Y(mean))^2
1
50
161
8050
2500
201.28
15.88
1959.54
2
71
1938
137598
5041
410.51
42124.70
3002364.80
3
55
57
3135
3025
251.10
2100.48
21983.00
4
50
31
1550
2500
201.28
15.88
30368.87
5
33
11
363
1089
31.91
30053.90
37739.54
6
58
14
812
3364
280.99
5733.63
36582.94
7
79
44
3476
6241
490.22
81195.97
26006.94
8
26
16
416
676
-37.84
59099.26
35821.87
9
69
278
19182
4761
390.58
34342.21
5290.14
10
44
47
2068
1936
141.50
4065.95
25048.34
11
37
180
6660
1369
71.76
17824.28
638.40
12
70
22
1540
4900
400.55
38134.19
33586.67
13
20
52
1040
400
-97.62
91738.06
23490.67
14
45
194
8730
2025
151.47
2894.61
126.94
15
49
34
1666
2401
191.32
194.56
29332.27
Sum
756
3079
196286
42228
409533.57
3310340.93
Average
50.4
205.2667
b
9.963254
a
-296.881
Coefficient of Determination is R^2 = (Sum of Squares of Regression)/(Sum of Squares Total)
R^2 = SSR/SST
SSR = (Y(cap)-Y(mean))^2
SST = (Y-Y(mean))^2
R^2 = 409533.57/3310340.93
= 0.123713.
Regression Equation is
Y = bX + a
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