HESA 6505 Lecture Notes - Lecture 11: Stepwise Regression, Model Selection

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crimsoncockroach314

5 Dec 2017

School

Dalhousie University

Department

Health Administration

Course

HESA 6505

Professor

Hajizadeh

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Document Summary

R2 never decreased when a new x variable is added to the model. This can be a disadvantage when comparing models. Shows the proportion of variation in y explained by all x variables adjusted for the. F test for overall significance of the model. Shows if there is a linear relationship between all of the x variables considered together. Shows if there is a linear relationship between the variable xj and y holding constant th. A dummy variable is a categorical independent variable with two levels: Assumes the slopes associated with numerical independent variables do not change wit. If more than two levels, the number of dummy variables needed is (number of levels -- The number of dummy variables is one less than the number of levels/categories. The aim of selection is to reduce the set of predictor variables to those that are necessa.

Related Questions

ECON 3050

Q24. The coefficient of determination (r²) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of YË in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than â0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

yellowturtle964

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

For the record, this is a homework question. A statistics student wishes to understand the relationship between a used car's price and the number of miles that car has been driven. The student goes to a local car lot and writes down the prices and the odometer reading for 100 cars. The student takes this information and completes a regression. The goal is to examine how the miles drove impacts the car's price. The regression output appears at the end of this assignment. Use the output to answer the following questions.

a) (3 points) Dependent variables Independent variable

b) (8 points) Do you expect a positive, negative, or no relationship between miles driven and price? Draw a scatterplot that corresponds to your relationship.

Be sure to include which variable (miles or price) is on the x-axis and which is on the y-axis.

b) (3 points) Write the regression equation (I want the specific estimates for the coefficients)

c) (3 points) What is the interpretation of the slope coefficient of b 1 (in terms of this problem)?

d) (4 points) Is b 1 significant from zero? How do you know?

e) (3 points) Use the regression equation to predict the price for a car that was driven for 30,000 miles. Is this mileage appropriate to make a prediction? Why or why not?

f) (3 points) Use the regression equation to predict the price for a car that was driven for 80,000 miles. Is this mileage appropriate to make a prediction? Why or why not?

g) (3 points) What percentage of price variation is explained by the variation in miles driven?

Multiple R 0.398635

R square 0.15891

Adjusted R Squared 0.150327

Standard Error 1481.414

Observations 100

df ss ms f significance f

Regression 1 40633716.14 40633716 18.51542325 3.99E-05

Residual 98 215069573.5 2194587

Total 99 255703289.7

coefficient standard error t stat p value lower 95%

intercept 20261.42 598.0313643 33.8802 6.53E-56 19074.64824

x1 -0.07332 0.017039697 -4.30296 3.99E-05 -0.107135778

Sample range for Y 14281 20511

Sample range for X 19100 49200

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HESA 6505 Lecture Notes - Lecture 11: Stepwise Regression, Model Selection

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