ECON 2P91 Lecture Notes - Statistical Hypothesis Testing, Sampling Distribution, Confidence Interval

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lemonrabbit637

3 Oct 2014

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Simple linear regression model y i b b x i. Model assumes direction of causality runs from x to y. is the intercept parameter (i. e. the value of the dependent variable y when the. 0 b independent variable x is equal to zero) is the slope parameter (indicates the effect of increasing x by one unit on the. 1b dependent variable); indicates a positive relationship; and. 0 b indicates no relationship between x and y; 1 is negative indicates a negative relationship b. For the model y i b b x i. 2 x is the ols estimator for b. 1 x is the ols estimator of b. One property of predicted values: mean of predicted values of dependent variable is always equal to mean of actual values of the dependent variable when an intercept is included in the model i. e. n b n. Two properties of residuals: mean of residuals is always equal to zero when an intercept b.

Related Questions

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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ECON 2P91 Lecture Notes - Statistical Hypothesis Testing, Sampling Distribution, Confidence Interval

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