16. Crickets, part of the family Orthoptera (including grasshoppers and katydids
ID: 3241065 • Letter: 1
Question
16. Crickets, part of the family Orthoptera (including grasshoppers and katydids) are known for their chirping. The frequency of chirping (number per second, x) varies according to temperature (y) is given by the equation:
y= 3.5 x + 25
a. What is the predicted temperature for a cricket that chirps 14 times per second?
b. What is the predicted temperature for a cricket that chirps 16 times per second?
c. What is the predicted temperature for a cricket that chirps 17 times per second?
d. What is the predicted temperature for a cricket that chirps 20 times per second?
e. Use the table below to find the Sum of Squared Error (SSE = SSE =Ee2) for the data points below and the above equation.
Chirps (X) Temperature (Y) 14 76 16 83 17 81 17 83 20 93Explanation / Answer
We are given,
y^ = 3.5x + 25
Question a)
X = 14
y^ = 3.5x + 25
= (3.5*14)+25
= 74
Answer: 74
Question b)
X = 16
y^ = 3.5x + 25
= (3.5*16)+25
= 81
Answer: 81
Question c)
X = 17
y^ = 3.5x + 25
= (3.5*17)+25
= 84.5
Answer: 84.5
Question d)
X = 20
y^ = 3.5x + 25
= (3.5*20)+25
= 95
Answer: 95
x
y
14
76
16
83
17
81
17
83
20
93
We go to excel. We go to Data then Data Analysis. There we go to regression. We select x and y. Finally clink on OK. We get the regression output where we find the value SSE.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.955
R Square
0.913
Adjusted R Square
0.883
Standard Error
2.110
Observations
5
ANOVA
df
SS
MS
F
Significance F
Regression
1
139.438
139.438
31.307
0.011
Residual
3
13.362
4.454
Total
4
152.8
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
37.447
8.231
4.549
0.020
11.251
63.643
X Variable 1
2.723
0.487
5.595
0.011
1.174
4.272
Answer: The value of Sum of Squared Error is 13.362
x
y
14
76
16
83
17
81
17
83
20
93
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