Question

What is the relationship between the price of crude oil and the price you pay at the pump for​ gasoline? The accompanying table shows the prices of crude oil and the price you pay at the pump for 24 consecutive months. Complete parts​ (a) through​ (h) below.

Month   Crude_Oil   Gasoline
1   75   1.858
2   76   1.477
3   75   1.372
4   76   1.204
5   75   2.344
6   75   2.424
7   78   1.399
8   81   1.296
9   74   1.496
10   79   1.196
11   81   1.204
12   78   2.213
13   79   2.073
14   80   2.184
15   82   2.281
16   83   2.039
17   81   2.647
18   78   2.585
19   74   2.881
20   79   2.766
21   83   2.696
22   84   3.205
23   84   3.006
24   85   3.272

part a) Construct a scatter plot with the crude oil cost​ (in dollars) on the horizontal axis and the gasoline cost​ (in dollars per​ gallon) on the vertical axis. Choose the correct graph below.

part b) Use the​ least-squares method to develop a simple linear regression equation to predict the gasoline prices using the average crude oil cost as the independent variable. (explain how to find using phstat)

part c) Interpret the meaning of the​ slope, b1​, in this problem.

part D) Plot the residuals versus the time period.

part e) Compute the​ Durbin-Watson statistic. (on PHSTAT)

part f) At the 0.05 level of​ significance, is there evidence of positive autocorrelation among the​ residuals?

part g) Based on the results of​ (d) through​ (f), is there reason to question the validity of the​ model?

part H) What conclusions can you reach concerning the relationship between the price of a barrel of crude oil and the price of a gallon of​ gasoline?

Answer 1

We will do this problem with the help of Excel.

part a) Construct a scatter plot with the crude oil cost​ (in dollars) on the horizontal axis and the gasoline cost​ (in dollars per​ gallon) on the vertical axis. Choose the correct graph below.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Scatterplot.

Select crude oil cost​ as the horizontal axis.

Select gasoline cost as the vertical axis.

Click OK.

The output will be as follows:

part b) Use the​ least-squares method to develop a simple linear regression equation to predict the gasoline prices using the average crude oil cost as the independent variable. (explain how to find using phstat)

From the scatterplot, we have the simple linear regression equation:

y = -4.464 + 0.084*x

Or

Gasoline Cost = -4.464 + 0.084*Crude Oil Cost

part c) Interpret the meaning of the​ slope, b1​, in this problem.

A simple linear regression equation has a form:

y = b₀ + b₁*x

We have our simple linear regression equation:

y = -4.464 + 0.084*x

b₁ = 0.084

This means that for an increase in every one dollar of Crude oil, Gasoline cost will increase by 0.084 dollars.

part D) Plot the residuals versus the time period.

Load the data into Excel.

Go to Data>Megastat.

Select the option Correlation/Regression and go to Scatterplot.

Select crude oil cost​ as the independent variable, x.

Select gasoline cost as the dependent variable, y.

Select Plot residuals by observation.

Click OK.

The output will be as follows:

As HOMEWORKLIB answering guide, we have the option to answer only the first four sub-parts of a question when there are more than four parts. If you want me to answer the rest of the parts, please post the question in a new post. Thank You!