The chief financial officer of a major service company has...

The chief financial officer of a major service company has asked you to develop a regression model to predict consumption of service goods as a function of GDP and other important variables. The data for your analysis are found in the data file Macro2010, which is stored on your data disk and described in the data dictionary in the chapter appendix. Use data from the period 1980.1 through 2010.4. a. Estimate a regression model using only GDP to predict consumption of service goods. Test for autocorrelation using the Durbin-Watson statistic. b. Estimate a multiple regression model using GDP, total consumption lagged 1 period, imports or services, and prime interest rate as additional predictors. Test for autocorrelation. Does this multiple regression model reduce the problem of autocorrelation?

The chief financial officer of a major service company has asked you to develop a regression model to predict consumption of service goods as a function of GDP and other important variables. The data for your analysis are found in the data file Macro2010, which is stored on your data disk and described in the data dictionary in the chapter appendix. Use data from the period 1980.1 through 2010.4.
a. Estimate a regression model using only GDP to predict consumption of service goods. Test for autocorrelation using the Durbin-Watson statistic.
b. Estimate a multiple regression model using GDP, total consumption lagged 1 period, imports or services, and prime interest rate as additional predictors. Test for autocorrelation. Does this multiple regression model reduce the problem of autocorrelation?

Key Concepts

Durbin-Watson Statistic

The Durbin-Watson statistic is used to test for first-order autocorrelation in the residuals from a regression analysis. It helps identify whether sequential error terms are correlated, thus signaling potential issues with the model's assumptions regarding error independence.

Lagged Variables

Lagged variables are previous values of a variable used as predictors in a regression model. Incorporating lagged values is common in time series analysis to capture the delayed effects of predictors on the dependent variable, which can improve the model's explanatory power.

Time Series Analysis

Time series analysis is the study of data points collected or recorded at specific time intervals. It focuses on understanding underlying patterns such as trends, seasonality, and cycles, and is particularly crucial when the data are sequential in nature, which is common in economic and financial studies.

Multiple Regression Analysis

Multiple regression extends the concept of simple regression by incorporating more than one independent variable. This approach allows for a more comprehensive model that can account for the influence of several factors simultaneously, thereby providing a better fit and deeper insight into the relationships between variables.

Autocorrelation

Autocorrelation refers to the correlation of a time series with its own past values. In regression analysis, it indicates that the error terms are not independent of each other, which can bias the estimates of standard errors and compromise the validity of statistical tests.

Simple Linear Regression

Simple linear regression involves modeling the relationship between a dependent variable and a single independent variable. This method helps in understanding how changes in the predictor affect the outcome and serves as a foundational tool for statistical analysis in various fields, including economics.

Transcript

00:03 Okay, for this problem, we're given some information about cost and production volume for some manufacturing.

00:14 So i'm going to write out what we want to find here first, and we're going to work our way and use excel to figure these things out.

00:23 So for part a, just to plan ahead, we want to find a regression equation.

00:29 So we want to find a regression equation.

00:31 We're going to use our excel to do that.

00:33 You could also use the graph and calculator.

00:37 So with the regression equation, i usually use y equals a plus bx.

00:47 And then in part b, we want to find out what is the cost per unit produced.

00:57 And really that's the average cost per unit, part c.

01:00 We want to find what's called the coefficient of determination.

01:04 The coefficient of determination is the r squared value.

01:08 And then finally we're going to say, what if situation, we make regression equations to figure out what happens if we have a certain number of units.

01:15 So we'll have a model and then we're going to say, well, what if we have x equals to 500 units? what will the cost be? so let's go over here.

01:25 So the first thing i have to put in some data.

01:29 So i'm going to my excel.

01:31 And if you have time, you can kind of give it a nice title.

01:34 I'm just going to list this out because you see it in your book.

01:37 But production volume units.

01:39 So it's 400, 450.

01:43 And it's nicely going up.

01:48 It wasn't, it doesn't matter.

01:49 Excel can still do the best fit line and the regression equation, regardless of it being in order.

01:54 So the total cost is 4 ,000, 400 units, and then 5 ,000, and so on.

02:04 So what we're going to do is we're going to let excel do a little to work for us and figure out the regression equation.

02:10 So we can answer all these questions on the average increase and i'll look at the coefficient of determination.

02:20 So there's different ways to get this to happen.

02:22 But good news is i have, my values from my textbook here.

02:28 I'm going to make a table here.

02:34 Let's see, let's insert.

02:36 I go old school on this.

02:37 I go insert and i look for all these different graphs.

02:41 Well, when i use the most, we're gonna do like a scatter plot.

02:47 So there's our scatter plot.

02:48 We don't wanna connect the lines, okay? so since it made a table for us, you might as well give it the title.

02:54 So this is production volume.

02:57 Keep it simple.

03:08 Production volume.

03:15 And so what we want to do is like if we had a ruler, just put a ruler between these guys here.

03:19 But what we do in excel, there's different ways to do it.

03:22 But i click on the data, and then i just do what's called add a trend line.

03:26 So i right click on the data.

03:28 Do add a trend line...

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