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

- Define the explanatory and response variables for this problem.
- 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 - In a brief sentence, interpret the
**slope in the context of the problem**. **Predict**the price in dollars per thousand cubic feet**for the month of October (the 10**for this month.^{th}month)

Then calculate the residual- What is the correlation coefficient? Is the linear association
between the variables “weak” or “strong”?

**How do you know?** - 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. - 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")

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