ECON 6306 Lecture Notes - Lecture 7: Dependent And Independent Variables, General Linear Model, Coefficient Of Determination

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pearjellyfish746

8 May 2018

School

UT-Dallas

Department

Economics

Course

ECON 6306

Professor

Dr. Michael Tiefelsdorf

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Multivariate Regression

Previously, we considered that y variable

was affected only by the change in one x

variable. In reality, that is almost never

the case. Many x variables are jointly

affecting the dependent variable. Starting

off, we run into a problem. We are trying

to measure the effect of x on y. But it is

almost always the case that the x

variables are also correlated among each

other. In the figure to the right, the top

left diagram shows this phenomena. Both

x1 and x2 not only affect y but also each

other. The ideal scenario for us is given in

the bottom left where there is no

correlation between the two x variables.

An extreme case is given in the bottom

right where x1 and x2 are strongly

correlated. This can be a problem in our regression model and is called multicollinearity. The good news is that

the problem of correlation and multicollinearity is fixable through our regression models.

Partial regression coefficients

Even if there is correlation between x1 and x2, the regression coefficients can be calculated. We can get the

effect of x1 on y while controlling for the effect of x2 on y. This means that the estimate we get for the slope

related to x1 is independent of the value of x2. In other words, for any value of x2, the effect of x1 stays

constant. R does this for us automatically.

Interpreting coefficients

To run a multivariate regression model, use the following snippet of code as an R script.

model1 <- lm(Petal.Length~Sepal.Width+Sepal.Length, data = iris)

summary(model1)

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Document Summary

Previously, we considered that y variable was affected only by the change in one x variable. In reality, that is almost never the case. Many x variables are jointly affecting the dependent variable. We are trying to measure the effect of x on y. But it is almost always the case that the x variables are also correlated among each other. In the figure to the right, the top left diagram shows this phenomena. Both x1 and x2 not only affect y but also each other. The ideal scenario for us is given in the bottom left where there is no correlation between the two x variables. An extreme case is given in the bottom right where x1 and x2 are strongly correlated. This can be a problem in our regression model and is called multicollinearity. The good news is that the problem of correlation and multicollinearity is fixable through our regression models.

Related Questions

We know that regression analysis relates to the correlation rather than causation between variables. A critical step in this analysis is the selection of the variables to be related. If you do not select the most relevant variables the results would likely not be very useful in making a business decision.

Read and study the following scenario and then respond to the assignment criteria.

You own a hotdog stand outside of a major college football stadium. You have been at the same location for 5 years and your competitors remain the same. Your pricing strategy also remains the same. Your margins are thin and as such if you do not sell the hotdogs you cooked you lose money, and if you do not cook enough hotdogs to meet the demand you lose revenue.

Your task then is to determine how many hotdogs you should prepare for each game. You decide to use regression analysis based on historical data to project how many hotdogs you should prepare. The critical decision is to select the most relevant variables that impact how many hotdogs you sell during a game.

Write responses to the following:

1.Start by recognizing that the dependent variable is the number of hotdogs sold.

2.Identify at least 4 possible independent variables that might influence the dependent variable, and explain how each variable might correlate to the dependent variable.

3.From the 4 possible independent variables select the two most relevant variables and explain why they are more relevant than the two you did not select.

4.Finally, describe how these two variables would be correlated to the dependent variable and could there be any correlation between these two independent variables.

ultramarinecat93

1. Novo Nordisk A/S, a Danish firm, sells insulin and other drugs worldwide. Activella, an estrogen and progestin hormone replacement therapy sold by Novo-Nordisk, is examined using 33 quarters of data

Y = -204+.34X1-.17X2

(17.0) (-1.71)

Where Y is quarterly sales of Activella, X1 is the Novo's advertising of the hormone therapy, and X2 is the advertising of a similar product by Eli Lilly and Company, Novo-Nordisk's chief competitor. The parentheses contain t-values. Addition information is: Durbin-Watson = 1.9 and R2= .89. According to t distribution table , t .05,31=1,6955

Using the data for Novo-Nordisk, which is correct?

A. Both X1 and X2 are statistically significant.

B. Neither X1 nor X2 are statistically significant.

C. X1 is statistically significant but X2 is not statistically significant.

D. X1 is not statistically significant but X2 is statistically significant.

E. The Durbin-Watson statistic shows significant problems with autocorrelation.

2. Which is NOT true about the coefficient of determination?

A. As you add more variables, the R-square generally rises.

B. As you add more variables, the adjusted R-square can fall.

C. If the R-square is above 50%, the regression is considered significant.

D. The R-square gives the per cent of the variation in the dependant variable that is explained by the independent variables.

E. The higher is the R-square, the better is the fit.

3. Table: Sherwin-Williams Company new Data

Observations Sales Promotional Expenditures Selling Price Disposable Income

I y A P M

1 160 100 15 19

2 200 160 14 17.5

3 140 50 16.5 14

4 190 190 14.5 20

5 130 90 17 15.5

6 160 70 16 14.5

7 200 140 15 21.5

8 150 110 18 18

9 210 200 12 18.5

10 190 100 15.5 20

Total 1750 1250 151 179.5

Mean 175 125 15.1 17.95

A. What is the regression equation for paint sales using a multiple linear regression model?

B. If A=180, P=$14, and M= 20, what is an approximate 95 per cent prediction interval for paint sales?

harlequinsardine5

Question 1

Which of the following approaches to understanding and predicting consumer behavior depends primarily on the knowledge and experience of a firm's employees and its suppliers?

		Test marketing and price experiments
		Analysis of historical data.
		Direct consumer surveys.
		Expert opinion.

Question 2

In which of the following situations would reliance on expert opinion as a basis for a managerial decision be most preferred?

		When the product being marketed is relatively new.
		When the level of economic activity can have a significant effect on the demand for the firm's output.
		When the product can be packaged with a variety of price and quality combinations.
		When the business in question serves as a supplier of inputs to other businesses, especially in multi-product situations where other strategies may be prohibitively expensive.

Question 3

The approach to analyzing consumer behavior that asks consumers to rank and choose among different product attributes to reveal their relative valuation of different characteristics is called:

		conjoint analysis.
		contingent valuation.
		the hedonic estimation technique.
		a direct consumer survey.

Question 4

All of the following are limitations of direct consumer surveys except:

		the possibility of response biases because survey respondents may not want to reveal their true preferences.
		the possibility that the type of questions asked may unintentionally bias the respondent's answers.
		the likelihood that respondents will deliberately and systematically mislead interviewers.
		the possibility that consumers' responses may not reflect their actual behavior in the market place.

Question 5

Which of the following approaches to understanding and predicting consumer behavior does not actually solicit any information from potential customers?

		Expert opinion.
		Test marketing.
		Analysis of historical data.
		Conjoint analysis.

Question 6

Data collected on a sample of individuals with different characteristics at a specific point in time are called:

		panel data.
		cross-section data.
		time series data.
		none of the above.

Question 7

Which of the following approaches to understanding and predicting consumer behavior provides the most insight into how consumers can be expected to respond in an actual market setting?

		Test marketing.
		Conjoint analysis.
		Expert opinion.
		Analysis of historical data.

Question 8

An approach to analyzing consumer behavior in which consumer reaction to different prices is analyzed in a laboratory situation or a test market is called:

		non-price experiments.
		focus groups.
		price experiments.
		none of the above.

Question 9

Data collected on the same observation unit at a number of points in time are called:

		panel data.
		time series data.
		cross-section data.
		none of the above.

Question 10

A measure of how much the coefficient would vary in regressions based on different samples is called:

		F-statistic.
		standard error of the estimated coefficient.
		t-statistic.
		partial F-statistic.

Question 11

The test statistic used to test the hypothesis of whether a regression coefficient is significantly different from zero, holding all other independent variables constant, is called a(n):

		t-test.
		F-test.
		multicollinearity test.
		autocorrelation test.

Question 12

Regression analysis that analyzes the relationship between one dependent variable and several independent variables is called:

		cluster analysis.
		correlation analysis.
		multiple regression analysis.
		simple regression analysis.

Question 13

The ratio of the regression coefficient to its standard error is called:

		F-statistic.
		t-statistic.
		coefficient of determination.
		partial F-statistic.

Question 14

The coefficient of determination will range between what values?

		-1 and +1
		0 and 1
		-3 and +3
		none of the above

Question 15

The range of values in which we can be confident that the true regression coefficient lies within a given degree of probability is called a:

		confidence interval.
		logistic regression.
		prediction interval.
		none of the above.

Question 16

The estimated regression equation is Y = 10 + 2.5X, if X =0 than the predicted value of Y is equal to

		2.5
		7.5
		12.5
		10

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ECON 6306 Lecture Notes - Lecture 7: Dependent And Independent Variables, General Linear Model, Coefficient Of Determination

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