Question

Biologists have observed that there is a linear relationship between the ambient temperature and the frequency at which a cricket chirps. Suppose that the follow data was measured for a particular species of cricket.

Temperature ∘∘F (x)(x)		Chirps per Second (y)(y)
92.0		20.2
85.0		18.6
89.1		19.3
88.4		19.9
77.5		15.9
88.0		18.4
83.6		18.1
86.7		19.4
84.9		18.6
78.9		16.8
72.9		15.5
90.6		20
90.6		20.1
96.5		20.9
75.5		15

a) What is the equation for the least squares line for this data?

y=
b) How many chirps per second would you expect to hear from this cricket if the ambient temperature was 55∘55∘F?

c) What is the ambient temperature if the cricket chirps 17.2 times per second?

d) What is the correlation coefficient?
r=

Answer 1

data -> data analysis -> regression in excel

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.969573574
R Square	0.940072915
Adjusted R Square	0.935463139
Standard Error	0.469987406
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	45.04578723	45.04578723	203.9302916	2.52793E-09
Residual	13	2.871546102	0.220888162
Total	14	47.91733333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-4.66049409	1.62264531	-2.872158236	0.013088823	-8.166006157
Temperature ∘∘F (x)(x)	0.270744736	0.018959163	14.28041637	2.52793E-09	0.229785956

a)

y^= -4.6605 + 0.2707 * x

b)

when x = 55

y^= -4.6605 + 0.2707 * 55

10.2304664

c)

17.2 = -4.6605 + 0.2707 * x

x = 80.7554

d)

r = 0.969573574