There is a regression relationship between y and at least one of the three independent variables. The estimated return for FSPTX when the growth index returns 1% and the value index returns -2% is 2.3%. We cannot reject that the growth index is statistically significant, but we can reject that the value index is statistically significant. The estimated return for December is 3.01% and for January is 3.04%. We can reject July, September, and October as being statistically insignificant. We cannot reject all months as being statistically insignificant, so at least one month is significant. The model predicts a UER of 5.304 for July 1996. The mean absolute deviation of

1. Quantitative Analysis for Business Lecture 8 August 30th, 2010 http://www.slideshare.net/saark/ibm401-lecture-8

2. Multiple regression exercise When the null hypothesis, H0: b1 = b2 = b3 = 0, is rejected, the interpretation should be: There is no linear relationship between y and any of the three independent variables There is a regression relationship between y and at least one of the three independent variables All three independent variables have a slope of zero All three independent variables have equal slopes There is a regression relationship between y and all three independent variables What is the difference between R2 and the adjusted R2? The adjusted R2 always increases as more independent variables are added to the model The adjusted R2 is smaller in this case because the constant term is negative The adjusted R2 adjusts explanatory power by the degrees of freedom The adjusted R2 is always smaller than R2 The adjusted R2 adjusts explanatory power by division by the standard error of each coefficient

3. Example 2 Suppose you are considering an investment in the Fidelity Select Technology Fund (FSPTX), a US mutual fund specializing in technology stock. You estimated the regression as Where Yt = monthly return on FSPTX X1t = monthly return to S&P500/BARRA Growth Index X2t = monthly return to S&P500/BARRA Value Index The estimated value for FSPTX when the return of the S&P500/BARRA Growth Index and the S&P500/BARRA Value Index are equal to 0 in a specific month is about 0.79%. The coefficient on the growth index return is 2.2308 and the coefficient on the value index return is -0.4143. What is the estimated return for FSPTX when the return of growth index is 1% and the return of the value index is -2%?

7. What is the estimated return for January?

9. Solution

10. Example 2 What is the estimated return for FSPTX when the return of growth index is 1% and the return of the value index is -2%?

13. Example 3 Can we reject any month for being statistically insignificant? Test individual variables  use t-test t-critical = 2.00 July (t-stat = -2.4686) September (t-stat = -2.2864) October (t-stat = -2.3966)

14. Example 3 Can we reject ALL month as being insignificant? Test ALL variables  use F-test F-stat < 1.87 Reject the Hypothesis that ALL months = 0 At least one month is significant

15. Example 4 Using the regression output, what is the model’s prediction of the UER for July 1996, midway through the first year of the sample period? UER = 5.5098 – 0.0294t The data began January 1996 July is period 7 UER(t=7) = 5.5098-0.0294(7) = 5.304

16. Example 4 What is the mean absolute deviation of 1st year estimation? UER = 5.5098 – 0.0294t

17. Example 4