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Write down a single equation linear model with one explanatory viariable using general notations (Y, beta0, beta1, X1, and epsilon) and identify dependent variable, independent variable, constant term, coefficient, and error term.

What can error term (e) potentially include? (Hint: 4 sources of variation in Y beside Xs')

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Nelly StrackeLv2

5 Jan 2019

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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

goldsnail303

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?

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