The data show the bug chirps per minute at different temperatures. Find the regr

Question

The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value?
Chirps in 1 min 1144, 842, 1211, 774, 809, 1134
Temperature (F) 86.7, 67.2, 90.2, 65, 68.6, 83.1
What is the regression Equation
Y^=______________+________________ round to the X- coefficient to four decimal places as needed. Round the constant to two decimal places as needed
What is the best predicted value
Y^= ______________(F).
What is wrong with this predicted value?
A. ) It is only an approximation. An unrou nded value would be considered accurate
B) it is unralistically high - the vale of 3000 is far outside the range of observed values
C) The first Variable should have been the dependent variable
D) Nothing is wrong with this value. It can be treated as an acurate prediction

Explanation / Answer

a)

XY and X2 as it was done in the table below.

the sum of every column:

X=5914 , Y=460.8 , XY=465042.2 , X2=6023734

using the formula for a and b

we get a = 21.83

and b = 0.05

y = 21.83+0.05x

b) fo x = 3000

y = 21.83 +0.05*3000

thereofore y = 171.83

c) the fact which is wrong with the pricited value is that the number of chips is unrealistically high hence option C is correct

X Y XY XX 1144 86.7 99184.8 1308736 842 67.2 56582.4 708964 1211 90.2 109232.2 1466521 774 65 50310 599076 809 68.6 55497.4 654481 1134 83.1 94235.4 1285956

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