Financial Time Series I and Methods of Statistical Prediction
Homework 4: Contingency table, regression, ANOVA Due Date: December 12th, 2002
1. For the 23 space shuttle flights that occurred before the Challenger mission Dis- aster in 1986, the following table shows the temperature (oF ) at the time of the flight and whether at least one primary O-ring suffered thermal distress.
Ft Temp TD Ft Temp TD Ft Temp TD
1 66 0 9 57 1 17 70 0
2 70 1 10 63 1 18 81 0
3 69 0 11 70 1 19 76 0
4 68 0 12 78 0 20 79 0
5 67 0 13 67 0 21 75 1
6 72 0 14 53 1 22 76 0
7 73 0 15 67 0 23 58 1
8 70 0 16 75 0
Here Ft= flight no., Temp= temperature, TD = thermal distress (1 = yes, 0 = no).
(a) Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the model fit.
(b) Calculate the predicted probability of thermal distress at 31o, the tempera- ture at the time of the Challenger flight. At what temperature does the predicted probability equal 0.5?
(c) Interpret the effect of temperature on the odds of thermal distress. Test the hypothesis that temperature has no effect, using the likelihood ratio test.
2. The following data is reported at 1991 General Society Survey at USA. The variables are gender and party identification. Subjects indicated whether they identified more strongly with the Democratic or Republic party or as Indepen- dents.
Party Identification
Gender Democrat Independent Republic Total
Female 279 73 225 577
Male 164 47 191 403
Total 444 120 416 980
Use Pearson Chi-Square test to test the null hypothesis of statistical indepen- dence of gender and party identification and report your conclusion.
3. Let Y1, . . . , Yn be independent random variables with distribution Yi ∼ N (µxi, σ2), i = 1, . . . , n,
where x1, . . . , xn are constants. Find the maximum likelihood estimators for µ and σ2, and find the distribution of ˆµ.
4. The following table gives the survival times (y) in hours after getting a poison for 12 sheep with different weights (x) in pounds. Analyze the data using a linear
regression model. Include a scatter plot of y versus x, a normal probability plot of residuals and provide the estimates for the intercept, slope, and the variance of Y with their standard errors. Make a report based on your analysis, respecting the following rules:
– Presentation of the problem and the data.
– Statistical analysis.
– Conclusions.
Refer to the last two pages for reference on a sample report.
x 46 55 61 75 64 75 71 59 66 67 60 63 y 44 27 24 24 36 36 44 44 36 29 36 36
5. A nationwide real estate brokerage house wants to study the relationship be- tween rent per square foot and the size of the property. The data collected are summarized in the following table.
Size of the Property (in square feet)
Location Less than 1, 000 1, 000 to 2, 000 2, 000 or more
Bad 3 2 3
4 5 6
So-so 5 5 7
5 6 7
Good 5 5 7
4 6 6
(a) Using these data, can we reject the null hypothesis that the average rent per square foot are equal?
(b) Redo the analysis without controlling the location factor, will it change the conclusion derived in (a)?
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