IBM401 Lecture 8
- 1. Quantitative Analysis for BusinessLecture 8August 30th, 2010http://www.slideshare.net/saark/ibm401-lecture-8
- 2. Multiple regression exerciseWhen 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 variablesThere is a regression relationship between y and at least one of the three independent variablesAll three independent variables have a slope of zeroAll three independent variables have equal slopesThere is a regression relationship between y and all three independent variablesWhat is the difference between R2 and the adjusted R2? The adjusted R2 always increases as more independent variables are added to the modelThe adjusted R2 is smaller in this case because the constant term is negativeThe adjusted R2 adjusts explanatory power by the degrees of freedomThe adjusted R2 is always smaller than R2The adjusted R2 adjusts explanatory power by division by the standard error of each coefficient
- 3. Example 2Suppose you are considering an investment in the Fidelity Select Technology Fund (FSPTX), a US mutual fund specializing in technology stock. You estimated the regression asWhereYt = monthly return on FSPTXX1t = monthly return to S&P500/BARRA Growth IndexX2t = monthly return to S&P500/BARRA Value IndexThe 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%?
- 4. Example 2Question: Is return to the S&P500/BARRA Value Index is statistically significant at 5% significant level? (t-critical at 5% is 2.00)
- 5. Is return to the S&P500/BARRA Growth Index is statistically significant at 5% significant level? (t-critical at 5% is 2.00)Example 3A researcher wants to know if returns to small stocks differ during various months of the year. Using data from Jan. 1979 to end of 2002, he estimated a regression including an intercept and 11 dummy variables, one for each of the first 11 months of the year. WhereEach monthly dummy variable has a value of 1 when the month occurs and 0 for the other monthsFirst observation is January
- 6. Example 3Question (F-critical = 1.87 and t-critical = 2)What is the estimated return for December?
- 7. What is the estimated return for January?
- 8. Can we reject any month for being statistically insignificant?Example 3Question (F-critical = 1.87 and t-critical = 2) Can we reject ALL month as being insignificant? Example 4The regression model below is an estimation of an unemployment rate (UER) 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?Example 4Using data below of 1996, What is the mean absolute deviation of 1st year estimation?
- 9. Solution
- 10. Example 2What is the estimated return for FSPTX when the return of growth index is 1% and the return of the value index is -2%?
- 11. Example 2 Cannot reject Growth and intercept
- 12. Reject ValueExample 3What is the estimated return for December?There is no dummy for DecemberSo the estimated return of December is when all other months = 0Rdec = 3.01% (intercept) What is the estimated return for January?Looking for January’s return, January = 1, other months = 0Rjan = 3.01 + 0.0003 = 3.04%
- 13. Example 3Can we reject any month for being statistically insignificant?Test individual variables use t-testt-critical = 2.00July (t-stat = -2.4686)September (t-stat = -2.2864)October (t-stat = -2.3966)
- 14. Example 3Can we reject ALL month as being insignificant?Test ALL variables use F-testF-stat < 1.87Reject the Hypothesis that ALL months = 0At least one month is significant
- 15. Example 4Using 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 – 0.0294tThe data began January 1996July is period 7UER(t=7) = 5.5098-0.0294(7) = 5.304
- 16. Example 4What is the mean absolute deviation of 1st year estimation?UER = 5.5098 – 0.0294t
- 17. Example 4