First Linear Relationship: Y=141-1.4x Second Linear Relationship: Y=139-1.3x Whe
ID: 3244976 • Letter: F
Question
First Linear Relationship: Y=141-1.4x
Second Linear Relationship: Y=139-1.3x
Where: x = Average Outdoor Temperature
y= Monthly Heating Bill
1 )Using the First Linear Relationship equation and the chart below, determine the sum of the squared residuals for the First Linear Relationship.
Avr. Outdoor Temp
Observed y
Fitted y
Residual
(Residual)2
45
80
32
95
25
110
30
90
35
85
=
2 )Using the Second Linear Relationship equation and the chart below, determine the sum of the squared residuals for the Second Linear Relationship.
Avr. Outdoor Temp
Observed y
Fitted y
Residual
(Residual)2
45
80
32
95
25
110
30
90
35
85
=
3) Based on the calculations of the Sum of Squared Residuals from Parts A and B, Which equation is a better fit for the given data? Why (be brief)?
Avr. Outdoor Temp
Observed y
Fitted y
Residual
(Residual)2
45
80
32
95
25
110
30
90
35
85
=
Explanation / Answer
We know that, Residual = (Observed y) - (Fitted y) __________________(1)
1)
Given that, Linear Relationship: Fitted Y=141-1.4X ____________________(2)
then table by abve linear relationship equation (1) and (2)
Avr. Outdoor Temp
x
Observed
y
Fitted
y
Residual
(Residual)2
45
80
78
2
4
32
95
96.2
-1.2
1.44
25
110
106
4
16
30
90
99
-9
81
35
85
92
-7
49
-11.2
151.44
2)
Given that, Linear Relationship: Fitted Y=139-1.3X ____________________(3)
then table by abve linear relationship equation (1) and (3)
Avr. Outdoor Temp
x
Observed
y
Fitted
y
Residual
(Residual)2
45
80
80.5
-0.5
0.25
32
95
97.4
-2.4
5.76
25
110
106.5
3.5
12.25
30
90
100
-10
100
35
85
93.5
-8.5
72.25
-17.9
190.51
3)
Based on the calculations of the Sum of Squared Residuals from Part A equation is a better fit for the given data Part B equation, because, the Sum of Squared Residuals of Part B is higher than Part A, i.e.,
(Sum of Squared Residuals of Part B) > (Sum of Squared Residuals of Part A)
190.51 > 151.44
As per Sum of Squared Residuals, the smaller the Sum of Squared Residuals, the better your equation is a better fit for the given data; The greater the Sum of Squared Residuals, the poorer your equation is a better fit for the given data.
Avr. Outdoor Temp
x
Observed
y
Fitted
y
Residual
(Residual)2
45
80
78
2
4
32
95
96.2
-1.2
1.44
25
110
106
4
16
30
90
99
-9
81
35
85
92
-7
49
SUM =-11.2
151.44
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