Question 2 (24 points; 36 minutes): An ordinary least squares regression of oper

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Question 2 (24 points; 36 minutes): An ordinary least squares regression of operating profits (PROFIT) for a sample of 50o recent start-up firms in Georgia on their dollar sales (SALES) and the number of employees (NEMP) yields: PROFIT-1143.9 0.439 SALES-34.44 NEMP, e R2 = 0.87 (2488.3) (0.0354) (6.510) where the figures in parentheses are the estimated standard errors of the estimates, i is the firm and ei is the estimated residual. All dollar values (PROFIT and SALES) are measured in $1000's. Note that: -1143.9 =-0.4597; 2488.4 0439 = 12.401; 00354 -34.44 = 5.290 6510 (a) (6 points) Interpret the results of the reported regression.

Explanation / Answer

2a. R-squared measures the closeness of the data to the fitted regression line. It is also known as the coefficient of determination.

R-squared = Explained variation / Total variation

In the given equation R square = 0.87 indicating that the model explains 87% of the variation of profit.

Calculating the P values for all the coefficients,

b0= 1143.9 p value = 0.3239 The p value is greater than 0.05 indicating that the intercept significantly contributes to the model

b1= 0.439 p value = 1 The p value is greater than 0.05 indicating that the coefficent of sales significantly contributes to the model

b2= 34.44 p value = 1The p value is greater than 0.05 indicating that the coefficent of Nemp significantly contributes to the model

b. heteroscedasticity refers to the instance in which the variability of a variable is unequal across the range of values of a second variable that predicts it. Regression is based on the assumption of homescedasity. This is actually a violation of the basic assumption of regression.

In ordinary least-squares (OLS) regression we seek to minimize residuals and in turn produce the smallest possible standard errors. OLS regression gives equal weight to all observations, but when the data has heteroscedasticity, the cases with larger disturbances have more influence than other observations. To overcome hetroscedasticity we need to use weighted least squares regression, this down-weights those observations with larger disturbances.

The result presented in the equation above need not be true, the variable with hetroscedasticity has more impact on the variable than the other variable. OLS does not provide the estimate with the smallest variance

2c. To overcome hetroscedasticity we need to use weighted least squares regression in place of normal OLS least square regression, this down-weights those observations with larger disturbances.

2d) This is a method to identify hetroscedacity. If the coeficients in the auxilary regression equation are significant we can say that hetroscedacity exist.

The intercept with value of -5980.7 and p value (calcualted using the ratio) of 0.152471 is not significant at significance level of 0.05

The sales with value of 2.374 and p value (calcualted using the ratio) less than 0.00001 is significant at significance level of 0.05

This indicates that the accountant's warning on presence of hetroscedacity is true and we need to use the weighted least square principle instead of OLS least square regression

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