Must Show Work- Can\'t use Matlab We observe from our campus the temperature and
ID: 3171176 • Letter: M
Question
Must Show Work- Can't use Matlab
We observe from our campus the temperature and count the number of squirrels.
Our obesrvations are
T= [52;52;50;54;50;52;54;80;80]
Sq= [8;10;6;9;6;12;12;1;0]
1)Can you make any statement or conclusion given these numbers as to the relationship of these paired observations?
3) Which aspect of the data is not being captured and does this affect the methodology of the straight line model used?
4) What is a good measure to assess the quality of the straight line fitted above? Use this measure
Explanation / Answer
T
C
T-TBAR
C-CBAR
(T-TBAR)^2
(C-CBAR)^2
(T-TBAR )* (C-CBAR)
52
8
6.22
(0.89)
38.72
0.79
(5.53)
52
10
6.22
(2.89)
38.72
8.35
(17.98)
50
6
8.22
1.11
67.60
1.23
9.14
54
9
4.22
(1.89)
17.83
3.57
(7.98)
50
6
8.22
1.11
67.60
1.23
9.14
52
12
6.22
(4.89)
38.72
23.90
(30.42)
54
12
4.22
(4.89)
17.83
23.90
(20.64)
80
1
(21.78)
6.11
474.27
37.35
(133.09)
80
0
(21.78)
7.11
474.27
50.57
(154.86)
58.22
7.11
1,235.56
150.89
(352.22)
a)
r is the correlation i.e. the relationship between Temperature and count of squirrel
r -0.815749814 summation(T-TBAR)^2/sqrt(summation(T-TBAR )* summation(C-CBAR))
=-0.8175
As temperature decreases then the count of squirrels will increase.
b)
sdy = sqrt (summation(C-CBAR)^2/(n-1))
= 4.3430
Sdx = sqrt (summation(T-TBAR)^2/(n-1))
= 12.428
Slope, a = r * sdy/sdx = -0.2851
Intercept, b
Y = ax + b
CBAR = A * TBAR + B
7.11 = -0.2851* 58.22 + B
B = 23.71
C = -0.2851*T + 23.71
Dependent variable is the count of squirrels and the independent variable is the temperature. Because the relation goes in a logical way i.e. the count of squirrels might increase or decrease based on the temperature whereas the statement that the temperature change is based on the count of squirrels doesn’t make sense.
c)
d) a Good method to test the fit is calculating r square. If the r-square is nearing 1, then all the variation in y is explained by x. in our example only 82% of the variation is explained, the rest of them is in the error or residual term
One other way is calculating the expected value of y using the equation. Subtracting it from the original value and squaring it and taking the average. This is SSE the sum of squared deviations of the error.
T
C
T-TBAR
C-CBAR
(T-TBAR)^2
(C-CBAR)^2
(T-TBAR )* (C-CBAR)
52
8
6.22
(0.89)
38.72
0.79
(5.53)
52
10
6.22
(2.89)
38.72
8.35
(17.98)
50
6
8.22
1.11
67.60
1.23
9.14
54
9
4.22
(1.89)
17.83
3.57
(7.98)
50
6
8.22
1.11
67.60
1.23
9.14
52
12
6.22
(4.89)
38.72
23.90
(30.42)
54
12
4.22
(4.89)
17.83
23.90
(20.64)
80
1
(21.78)
6.11
474.27
37.35
(133.09)
80
0
(21.78)
7.11
474.27
50.57
(154.86)
58.22
7.11
1,235.56
150.89
(352.22)
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