Chapter 6 #5- a, b, c, d Do towns in Massachusetts with higher elevations tend to...

Chapter 6 #5- a, b, c, d

Do towns in Massachusetts with higher elevations tend to get more snowfall? To answer this question, a random sample of five towns in Massachusetts, their average yearly snowfall (in inches), and elevation (in feet) were recorded in Table 6.9.

Town	Average Snowfall (Inches)	Elevation (Feet)
Boston	43.8	141
Amherst	37.0	295
Springfield	40.5	70
Pittsfield	62.1	1,039
Lowell	61.6	102

a) Draw a scatterplot and find the equation for the line of best fit.

b) Find the residual for Springfield.

c) Interpret whether or not you believe there is a significant relationship between the average snowfall and elevation in Massachusetts.

d) Find and interpret a 95% confidence interval for the true population slope parameter.

Expert Solution

(a)

The line of best fit is y = 0.0152x + 43.989

(b) For Springfield, y = 0.0152(70) + 43.989 = 45.05

Residual = 40.5 - 45.05 = -4.55

(c) The R^2 value is very low, and there is a low degree of association between elevation and snowfall. It is therefore most likely that no significant correlation exists between elevation and snowfall.

(d)

Regression Analysis

	r²	0.266	n	5
	r	0.516	k	1
	Std. Error	11.848	Dep. Var.	Average Snowfall (Inches)

ANOVA table
Source	SS	df	MS	F	p-value
Regression	152.5446	1	152.5446	1.09	.3738
Residual	421.1154	3	140.3718
Total	573.6600	4


Regression output					confidence interval
variables	coefficients	std. error	t (df=3)	p-value	95% lower	95% upper	std. coeff.
Intercept	43.9892						0.000
Elevation (Feet)	0.0152	0.0146	1.042	.3738	-0.0312	0.0617	0.516

The 95% confidence interval for the true slope is [-0.0312, 0.0617]. This includes 0. This confirms that elevation is not a significant predictor of snowfall. We are 95% confident that the true slope parameter lies in the above interval

orchestra answered 2 years ago

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