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# Regression Anaylsis

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1. Suppose

QD= 60 - 50PC

QS= -66 + 90PC

(a) Calculate the equilibrium price and quantity.

2. Interpret the results: of the following

Mutiple R 0.980
R square 0.961
Standard error 5.255
Observations 12.000

(i) determine significance of the model; (ii) determine significance of individual coefficients; (iii) compute elasticities; and (iv) interpret them.

https://brainmass.com/economics/elasticity/regression-anaylsis-292777

#### Solution Preview

1. QD= 60 - 50PC and QS= -66 + 90PC
At equilibrium QD=QS
so we have 60-50PC = -66+90PC
60+66 = (90+50)*PC
PC=126/140=0.90
Not substitute the value of PC to get the value of Q
QD=60-50*0.9=15
Thus, equilibrium price is \$0.90 and equilibrium quantity is 15.

2. (i) determine significance of the model;
Look at the ANOVA table,
ANOVA
Degrees of Sum of Mean Significance
Freedom Squares Square F-statistic of F-statistic
Regression 2.000 6051.510 3025.755 109.589 0.000000481
Residual 9.000 248.490 27.610
Total 11.000 6300.000

The F-statistics is 109.589 and the p-value for F-test is 0.000000481. Since the value of p is less than 0.01, we conclude that the model is significant at 1% significance level. The regression model as whole is statistically ...

#### Solution Summary

The equilibrium price and quantity are calculated.

\$2.19

## Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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