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Rainy Days 1
Use simple logistic regression to predict the probability of rain from temperature. Space Shuttles
Describe the relationship between the space shuttle temperature and O-ring thermal distress. |
Rainy Days 1: Problem |
A weather record was compiled for the month of April for a city in the eastern United States. The amount of rainfall (Precip), temperature (Temp), and barometric pressure (Pressure) were recorded for each of the 30 days of the month. A variable Rained was added to the set of data to categorize rainfall based on the following formula:
Rained ={"Rainy" if Precip > 0.02
{"Dry" otherwise
Fit a simple logistic regression function to the data to determine whether temperature is a significant predictor of the probability of rain based on this sample.
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Lee Creighton
SAS Institute
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Rainy Days 1: Sample Data | |
The Spring_rain data set is from a weather record for the month of April. The dataset contains information on the temperature, precipitation, and barometric pressure for each of the thirty days in the month. Also a categorical variable Rained is included which categorizes rainfall in the following manner:
Rained ={"Rainy" if Precip > 0.02
{"Dry" otherwise These are the variables in the data set: Name | Type | Description | | date | char | date given as mm/dd | | Temp | num | temperature | | Precip | num | amount of rainfall | | Pressure | num | barometric pressure | | Rained | char | categorical—if Precip > 0.02, then Rained = “Rained”; otherwise Rained = “Dry” | |
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Source of Data
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Sall, J., Creighton, L., & Lehman, A. (2006). JMP Start Statistics, Third Edition. Cary, NC: SAS Institute Inc. |
Rainy Days 1: Solution |
Based on the output generated by the LOGISTIC procedure in SAS, we find that the coefficient on temperature is very small (-0.00863) and the chi-square statistic is not significant (p-value=0.8707). So, we can conclude that temperature alone is not a significant predictor of the probability of rain.
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Space Shuttles: Problem |
In the 23 launches preceding the Challenger mission, data was collected recording the temperature at launch time and the presence or absence of O-ring thermal distress (coded as 0 for no distress, and 1 for distress). Find the equation for the logistic regression of the presence or absence of O-ring thermal distress on temperature at launch time. Determine whether launch-time temperature is a significant predictor for the probability of no distress. |
SAS Institute Inc.
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Space Shuttles: Sample Data | |
The O_ring data set contains data about temperature and O-ring thermal distress for the 23 space shuttle launches preceding the Challenger mission. These are the variables in the data set: Name | Type | Description | | flt | num | flight number | | temp | num | temperature at launch time | | td | num | indicator of whether or not there was thermal distress during the launch (0 for no distress, 1 for distress) | |
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Source of Data
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This data is sample data from SAS Institute Inc. |
Space Shuttles: Solution |
The probability modeled is for Td = 0 or no distress. Based on the parameter estimates, we have this logistic regression equation: ln[p/(1-p)] = -15.0429 +0.2322x The p-value for the test of significance is 0.0320. Therefore, at a level of α = 0.05, we can say that temperature at launch time is a significant predictor for the probability of no distress. |
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