Question

The following table shows data for the cost of natural gas in Maryland (in dollars per thousand cubic feet) for each month of the year 2018.

Month   Price in $ per Million Btu

1 8.38

2 7.99

3 7.73

4 8.20

5 8.73

6 8.99

7 9.25

8 9.30

9 10.65

10 8.19

11 8.69

12 9.69

1. Define the explanatory and response variables for this problem.
2. Use the calculator to obtain the linear regression line of best fit line; round to three decimal places.
   Write this prediction equation in the form: y-hat= a x+ b
3. In a brief sentence, interpret the slope in the context of the problem.
4. Predict the price in dollars per thousand cubic feet for the month of October (the 10^th month)
   Then calculate the residual for this month.
5. What is the correlation coefficient? Is the linear association between the variables “weak” or “strong”?
   How do you know?
6. Below, sketch a scatterplot comparing the Months in 2018 and Price per Thousand Cubic Feet. Draw your linear regression equation on this scatterplot. Label the axes and put a scale on the axes.
7. Use STATKEY to find the 5-number summary of the Natural Gas Price in Dollars per Thousand Cubic Feet. Then conduct an outlier test as defined by the OUTLIER FORMULA for Natural Gas Price in Dollars per Thousand Cubic Feet. and indicate any low or high outliers.   (Show all work)

Answer 1

a. Explanatory variable=Month, Response variable=Price in $ per Million Btu

b.

c. If one month is increased then expected price in $ per Million Btu is increased by 0.133.

d.

The linear association between the variables is “weak” (since value of correlation coefficient<0.6).

f.

R code:

x=1:12
y=c(8.38,7.99,7.73,8.20,8.73,8.99,9.25,9.30,10.65,8.19,8.69,9.69)
m=lm(y~x)
round(m$coefficients,3)#(b)
round(cor(x,y),4)#(e)
#(f)
plot(x,y)
lines(x,0.133*x+7.949,type="l")