DOC PREVIEW
UCSB ECON 240a - ONE WAY ANLYSIS

This preview shows page 1-2 out of 7 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 7 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Nov. 30, 2005 Lab #9 Econ240A-1 L. PhillipsOne-Way and Two-Way Analysis of Variance I. One-Way Analysis of VarianceA. ExcelOpen the data file xm15-01 that has data on weekly apple juice sales organized by advertising strategy: (1) convenience(city 1), (2) quality(city 2), (3) price(city 3). Go to the Tools menu, select Data Analysis, and in the dialog box, select Anova: Single Factor, and hit OK. In the next dialog box, for input range, type in A1:C21 (or select those cells). Check the box, labels in the first row. For output Options, select new worksheet ply. In the top panel, under averages, note the sample means for convenience, quality, and price. This is the data reported in Table 2 of the Lecture # 15 notes. In the bottom panel is the table of ANOVA, reported in Table 4 of these lecture notes.B. Eviews: One-Way ANOVA as Hypothesis TestingOpen the Eviews file, apple juice sales, in Eviews. Select salesaj, convenience, quality, price, and go to the menu and select view, open selected, one window, open group. Note that the sales data is stacked in a column of sixty observations, where the first twenty are for city one (convenience), the second twenty are for city two (quality), and the last twenty are for city 3 (price). Convenience is a dummy variable with ones for the first twenty observations and zeros for the last 40. Quality is a dummy variable with zeros for the first and last twenty observations, and ones for observations 21-40. Price is a dummy variable with zeros for the first forty observations and ones for the last twenty. Close this work-file window and select salesaj. Go to the menu and select view, open selected, one window. In the work-file window for apple juice sales that opens, go to the menu and select view, tests for descriptive stats, equality tests by classification.Nov. 30, 2005 Lab #9 Econ240A-2 L. PhillipsOne-Way and Two-Way Analysis of Variance In the dialog window that opens up, in the series/group for classify box, type in convenience quality price with a space between them, and hit OK. Note in the top panel, the F-statistic 3.23 with 2 degrees of freedom in the numerator and 57 in the denominator. In the second panel is the table of ANOVA, the same as in Table 4, of the Lecture notes # 15. The last panel shows the means for convenience, quality, and price, as well as other statistics, as reproduced in Table 2of these lecture notes.C. Eviews: Using Regression for One-Way ANOVAUse this file for apple juice sales to run a regression of salesaj convenience quality price, with no intercept. The regression results are reproduced as Table 5 of Lecture notes # 15. Note that the estimated coefficients on the three dummy, orindicator, variables are the mean sales of apple juice for the corresponding three cities. The F-statistic for the regression is 3.23, and the sum of squared residuals, 506983.5, is the same as the unexplained sum of squares in Table 4 of the lecture notes. The standard deviation of the dependent variable, 97.81474, squared and multiplied by 59, is the total sum of squares, 564496, reported in Table 4. The difference between this total and the unexplained is the explained sum of squares. So a table of ANOVA can be reproduced from this regression. Go to the view menu and select actual, fitted, residual-graph. Note the variation of actual sales around fitted sales (the mean level for convenience, then quality, then price) whichis the residual and an indication of the unexplained variance. To test the null hypothesis that the three means are equal, use the view menu to go to representations and observe that the three coefficients on the three dummy variables are denoted as C(1), C(2), and C(3). Use the view menu to goNov. 30, 2005 Lab #9 Econ240A-3 L. PhillipsOne-Way and Two-Way Analysis of Variance to coefficient tests, Wald-coefficient restrictions. In the Wald Test box that appears, type in C(1) =C(2) =C(3), and hit OK. Note that the F-statistic is 3.23, the same as for the regression and for the ratio of the explained mean square to theunexplained mean square in Table 4 of Lecture notes # 15.In this regression, the expected value of sales conditional on the dummy variables is:E (salesaj/convenience=1, quality=0, price=0) = convenience(1)E (salesaj/convenience=0, quality=1, price=0) = quality(2)E (salesaj/convenience=0, quality=0, price=1) = price(3) And the estimated parameters, C(1), C(2), and C(3), are the corresponding estimated sample means, as we saw from the regression. We could estimate the regression with a constant term and two of the dummy variables, say for convenience and quality:Salesaj = a + bc convenience + bq quality + e (4)In this case the expected value of sales, conditional on the values of the dummy variables including the intercept is:E (salesaj/a=1, convenience=0, quality=0) = a (5)E (salesaj/a=1, convenience=1, quality=0) = a + bc(6)E (salesaj/a=1, convenience=0, quality=1) = a + bq(7)As can be seen from running this regression the estimated intercept is the sample mean for price, the dummy variable that was omitted, as implied by the indicator variables for convenience and quality being zero, so:E (salesaj/a=1, convenience=0, quality=0) = a = price(8)E (salesaj/a=1, convenience=1, quality=0) = a + bc = convenience(9)E (salesaj/a=1, convenience=0, quality=1) = a + bq = quality(10)Thus, subtracting Eq. (8) from Eq. (9),Nov. 30, 2005 Lab #9 Econ240A-4 L. PhillipsOne-Way and Two-Way Analysis of Variance convenience - price = bc (11)and similarly, subtracting Eq. (8) from Eq. (10),quality - price = bq(12)so in this regression specification, the coefficients on the dummy variables capturethe difference in mean sales between the subgroup corresponding to that dummy variable and the mean sales for the subgroup for the omitted variable.Looking at the estimated regression for Eq. (4), there is no significant difference in sales between quality and price and/or between convenience and price. However, the biggest difference between means is between quality and convenience. Note that the F-statistic for the regression, 3.23, is significant, showing that at least two means differ. Repeat the regression for Salesaj = a + bq quality + bp price + e (13)Note that the coefficient on quality is significant, indicating a significant differencein mean sales between quality and convenience.II. Two-Way Analysis of VarianceA. ExcelOpen the data file xm15-03a in Excel. First we will conduct one-way


View Full Document

UCSB ECON 240a - ONE WAY ANLYSIS

Documents in this Course
Final

Final

8 pages

power_16

power_16

64 pages

final

final

8 pages

power_16

power_16

64 pages

Power One

Power One

63 pages

midterm

midterm

6 pages

power_16

power_16

39 pages

Lab #9

Lab #9

7 pages

Power 5

Power 5

59 pages

Final

Final

13 pages

Final

Final

11 pages

Midterm

Midterm

8 pages

Movies

Movies

28 pages

power_12

power_12

53 pages

midterm

midterm

4 pages

-problems

-problems

36 pages

lecture_7

lecture_7

10 pages

final

final

5 pages

power_4

power_4

44 pages

power_15

power_15

52 pages

group_5

group_5

21 pages

power_13

power_13

31 pages

power_11

power_11

44 pages

lecture_6

lecture_6

12 pages

power_11

power_11

42 pages

lecture_8

lecture_8

11 pages

midterm

midterm

9 pages

power_17

power_17

13 pages

power_14

power_14

55 pages

Final

Final

13 pages

Power One

Power One

53 pages

Summary

Summary

54 pages

Midterm

Midterm

6 pages

Lab #7

Lab #7

5 pages

powe 14

powe 14

32 pages

Lab #7

Lab #7

5 pages

Midterm

Midterm

8 pages

Power 17

Power 17

13 pages

Midterm

Midterm

6 pages

Lab Five

Lab Five

30 pages

power_16

power_16

64 pages

power_15

power_15

52 pages

Power One

Power One

64 pages

Final

Final

14 pages

Load more
Download ONE WAY ANLYSIS
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view ONE WAY ANLYSIS and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view ONE WAY ANLYSIS 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?