Question

In: Statistics and Probability

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.

Solutions

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
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


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