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25 Jan 2019

*** Please see p. 2 for Question 2 ***

Question 2 (7 points)

The following Excel output shows the outcome of a linear regression of individuals%u2019 wage per hour (in dollars) on the number of years they attended school (in years).

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.381932619

R Square

0.145872525

Adjusted R Square

0.144267022

Standard Error

4.753758428

Observations

534

ANOVA

df

SS

MS

F

Significance F

Regression

1

2053.22554

2053.22554

90.8578469

5.45998E-20

Residual

532

12022.25261

22.59821919

Total

533

14075.47815

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Upper 95.0%

Intercept

-0.745942699

1.045403804

-0.71354504

0.475821452

-2.799566599

1.307681201

1.307681201

Years of School

0.750448943

0.078729942

9.531938255

0.000545998

0.595789385

0.9051085

0.9051085

Part (a) (1 point)

What is the value of the estimated slope %u201Cb%u201D?

Part (b) (2 points)

Interpret the estimated value of the slope (i.e., explain what the number means in this regression).

Part (c) (1 point)

Is the estimate of the slope statistically significant? Please answer %u201Cyes%u201D or %u201Cno%u201D and explain how you can tell.

Part (d) (2 points)

Explain why we want to be able to reject the null hypothesis H0: %u03B2 = 0.

Part (e) (1 point)

How much of the total variation in wages can be explained by individuals%u2019 education?

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Lelia LubowitzLv2
28 Jan 2019

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Related questions

1. Write the subsequent demand equation, with Qd as the dependent variable; price, advertising, product development, and rel price as the independent variables.

2. How strong is the relationship between quantity demanded and the set of independent variables? List and explain 2 measures of this strength.

3. Which variable is most important in determining quantity demanded? Why?

Regression Statistics Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Multiple R 0.655864641 Ā  Ā  Ā  Ā  Ā  Ā  Ā 
R Square 0.430158427 Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Adjusted R Square 0.104534671 Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Standard Error 102678.3385 Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Observations 12 Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā 
ANOVA Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Ā  df SS MS F Significance F Ā  Ā  Ā 
Regression 4 55709596185 13927399046 1.321029008 0.349980066 Ā  Ā  Ā 
Residual 7 73799888386 10542841198 Ā  Ā  Ā  Ā  Ā 
Total 11 1.29509E+11 Ā  Ā  Ā  Ā  Ā  Ā 
Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā  Ā 
Ā  Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 1422378.519 1185014.572 1.200304665 0.269060955 -1379735.677 4224492.715 -1379735.677 4224492.715
X Variable 1 -247037.6649 160481.181 -1.539355975 0.167610603 -626515.3574 132440.0276 -626515.3574 132440.0276
X Variable 2 0.081609431 1.398101115 0.058371623 0.955083996 -3.22437437 3.387593232 -3.22437437 3.387593232
X Variable 3 -1.015253706 3.150288749 -0.322273222 0.756657161 -8.46450288 6.433995469 -8.46450288 6.433995469
X Variable 4 177211.9244 145755.2053 1.215818838 0.263460235 -167444.3689 521868.2176 -167444.3689 521868.2176

correlation:

Ā  medInc $ HS degree %
med inc 1 Ā 
HS degree % -0.033158666 1

regression:

multiple R .03315867
R Square .0010995
adjusted r sq -.0177477
standard error 6902.6743
observation 55
Ā  df ss ms f sig. f
regression 1 2779601.33 22779601.33 .05833749 .81007522
residual 53 2525286360 47646912.5 Ā  Ā 
total 54 25280659 Ā  Ā  Ā 
Ā  coefficients standard error t stat p-value lower 95% upper 95% lower 95.0% upper 95.0%
interpret 42273.3497 13809.7807 3.0611665 .00345814 14574.4373 69972.2621 14574.4373 69972.2621
hs degree -49.414226 204.587042 -.2415316 .81007522 -459.76387 360.935414 -459.76386 360.935414

a. very briefly interpret the estimated correlation coefficient...the direction and strength of the correlation

b. List and label the dependent variable and independent variable

c. based on regression results if a country's percentage of the population with at least a high school diploma increases by 1 by how much and in one direction does a country's median income change?

d. what is the predicted medinc for an HS degree of 70%

e. what proportion of the variation in medinc is explained by our regression model explained by variation in HS degree?

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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