PROBLEM 4 - PREDICTING CONSUMER CONFIDENCE

Situation:

The Conference Board produces a Consumer Confidence Index (CCI) that reflects people's feelings about general business conditions, employment opportunities, and their own income prospects. Some researchers may feel that consumer confidence is a function of the median household income. Shown here are the CCIs for nine years and the median household incomes for the same nine years published by the U.S. Census Bureau. Determine the equation of the regression line to predict the CCI from the median household income. Does median household income appear to be a good predictor of the CCI? Why or why not?

CCIMedian Household Income ($1,000)

116.837.415

91.536.770

68.535.501

61.635.047

65.934.700

90.634.942

100.035.887

104.636.306

125.437.005

Action

Perform a correlation and regression analysis to predict CCI using household income. Discuss the following:

a. Scatter Diagram

PLACE THE ANSWER FOR PART a IN THIS SECTION DESCRIBING THE DATA TREND WITH RESPECT TO SIGN OF THE SLOPE AND THE INTERPRETATION OF THS SLOPE OF THE REGRESSION EQUATION.

b. R, R2 and 1-R2

PLACE THE ANSWER FOR PART b IN THIS SECTION PROVIDING THE VALUES OF R, R2, AND 1-R2 AND INTERPRETATION OF EACH ONE OF THESE VALUES.

c. Show the regression equation. Comment on the interpretation of the slope of regression equation.

PLACE THE ANSWER FOR PART c IN THIS SECTION DESCRIBING THE REGRESSION EQUATION WITH RESPECT TO HOW WELL IT FITS THE DATA CONSIDERING THE VALUES COMPUTED IN PART b OF THE PROBLEM.

d. What is the standard error of estimate value? What is the interpretation of this value?

PLACE THE ANSWER FOR PART d IN THIS SECTION PROVIDING THE VALUE OF STANDARD ERROR OF ESTIMATE AND ITS INTERPRETATION.

e. Conduct the appropriate test of hypothesis for the regression model. Use a .05 level of significance. Does median household income appear to be good predictor of the CCI? Why or why not?

PLACE THE ANSWER FOR PART e IN THIS SECTION.SHOW THE Ho AND Ha.SHOW THE COMPUTED p-VALUE.COMPARE p-VALUE TO SIGNIFICANCE LEVEL AND STATE WHETER Ho SHOULD BE REJECTED BASED ON THIS COMPARISON.BASED ON WHETHER Ho IS/IS NOT REJECTED, STATE WHETHER MEDIAN HOUSEHOLD INCOME APPEARS TO BE A GOOD PREDICTOR OF CCI.

PROBLEM 5 - HOUSING PRICES

Situation:

Real Estate One conducted a recent survey of house prices for properties located on the shores of Tawas Bay. Data on 26 recent sales, including the number of bathroom, square feet and bedrooms are below.

Selling Price

Baths

Sq Ft

Beds

160000

1.5

1776

3

170000

2

1768

3

178000

1

1219

3

182500

1

1568

2

195100

1.5

1125

3

212500

2

1196

2

245900

2

2128

3

250000

3

1280

3

255000

2

1596

3

258000

3.5

2374

4

267000

2.5

2439

3

268000

2

1470

4

275000

2

1678

4

295000

2.5

1860

3

325000

3

2056

4

325000

3.5

2776

4

328400

2

1408

4

331000

1.5

1972

3

344500

2.5

1736

3

365000

2.5

1990

4

385000

2.5

3640

4

395000

2.5

1918

4

399000

2

2108

3

430000

2

2462

4

430000

2

2615

4

454000

3.5

3700

4

Action:

Use the data above and multiple regression to produce a model to predict the average sale price from other variables. Comment on the following:

a. Regression equation

PLACE THE ANSWER FOR PART a IN THIS SECTION DESCRIBING SHOWING THE REGRESSION EQUATION

b. R, R2 and 1-R2, adjusted R2

PLACE THE ANSWER FOR PART b IN THIS SECTION PROVIDING THE VALUES OF R, R2, AND 1-R2 AND INTERPRETATION OF EACH ONE OF THESE VALUES.

c. Standard error of estimate

PLACE THE ANSWER FOR PART c IN THIS SECTION PROVIDING THE VALUE OF STANDARD ERROR OF ESTIMATE AND ITS INTEPRETATION.

d. Report the t's for each value and the corresponding p-values

PLACE THE ANSWER FOR PART d IN THIS SECTION PROVIDING THE t VALUES AND CORRESPONDING p VALUES FOR EACH OF THE INDEPENDENT VARIABLES.

e. Overall test of hypothesis and decision

PLACE THE ANSWER FOR PART e IN THIS SECTION.SHOW Ho AND Ha FOR OVERAL TEST OF HYPOTHESIS.COMPARE p-VALUE TO SIGINFICANCE LEVEL AND STATE WHETER Ho SHOULD BE REJECTED BASED ON THIS COMPARISON.BASED ON WHETHER Ho IS/IS NOT REJECTED, STATE WHETHER THE EQUATION PROVIDED IN PART a OF THE PROBLEM IS A GOOD PREDICTOR OF THE PRICE OF A HOUSE

f. Use a .05 level of significance. Cite which variables are significant and which are not significant, based on the t values and p values for each independent variable.

PLACE THE ANSWER FOR PART f IN THIS SECTION.EXPLAIN WHETHER BATHROOMS, SQUARE FEET, AND BEDROOMS ARE SIGNIFICANT COMPARING THE APPROPRIATE p VALUE TO THE PROBLEM STATEMENT SPECIFIED SIGNIFICANCE LEVEL.