# R Programming Problems

Subject Mathematics Statistics-R Programming

## Question

Variables:

Column 1: datestring
Column 2: 0-3_hr_verification
Column 3: 3-6_hr_verification
Column 4: 6-9_hr_verification
Column 5: 9-12_hr_verification
Column 6: 0-6_hr_verification
Column 7: 6-12_hr_verification
Column 8: 0-12_hr_verification
Column 9: normalized_wind
Column 11: 700_mb_geos._dir
Column 12: 700_mb_geos._mag
Column 13: u_bar_at_den
Column 14: u_bar_at_location_
Column 15: 500-700_mb_geostrophic_shear
Column 16: 700_measured/700_geostrophic_wind
Column 17: 700_measured_-_700_geostrophic_wind
Column 18: relative_humidity
Column 19: cross-mountain_height_diff.
Column 20: static_stability_ratio
Column 21: froude_height
Column 22: scorer_parameter
Column 23: char._imped._ratio
Column 24: lowest_trop
Column 25: local_trop
Column 26: garbage_variable
Column 27: postfrontal_parameter
Column 28: sangster_parameter

Predictors:

Column 11: 700_mb_geos._dir
Column 12: 700_mb_geos._mag
Column 13: u_bar_at_den
Column 14: u_bar_at_location_
Column 15: 500-700_mb_geostrophic_shear
Column 16: 700_measured/700_geostrophic_wind
Column 17: 700_measured_-_700_geostrophic_wind
Column 18: relative_humidity
Column 19: cross-mountain_height_diff.
Column 20: static_stability_ratio
Column 21: froude_height
Column 22: scorer_parameter
Column 23: char._imped._ratio
Column 24: lowest_trop
Column 25: local_trop
Column 26: garbage_variable
Column 27: postfrontal_parameter
Column 28: sangster_parameter

1) Use an appropriate parametric test to determine if prefrontal and postfrontal windstorms have the same variance in peak wind speed. (α=0.05).

2) Formulate 95% bootstrap confidence intervals on the means of each of the individual predictors (Column 10-28, minus Column 26) for both the prefrontal windstorms and the postfrontal windstorms (separately). Use these results to determine which of the predictors are statistically significantly different between the prefrontal and postfrontal storms. Create a table with all confidence intervals to summarize the results (you can use any software you wish, including Excel, for this table). Briefly discuss the results.
- boot(dataset,statistic,R=1000)
- install.packages(‘boot’)
- library(‘boot’)
- mean.boot <- function(x,d) { return(mean(x[d])) }

3) Use an rbind to join the prefrontal and postfrontal predictor data (Column 10 – Column 28, omit Column 26) into a single matrix (by row). Also, join the prefrontal and postfrontal wind speeds (Column 8) into a single vector (use the c() function), and cbind that with the larger matrix. Your new matrix should have the same number of columns as your beginning dataset, plus 1, and its row dimensionality is equal to the number of cases.

4) Perform two separate stepwise regressions, one on the prefrontal data and one on the postfrontal data. Are the variables you kept the same for both? Which seems to be better based on the summary and ANOVA statistics?

5) Using your larger matrix you created at the beginning, do a classification to determine the following three predictors’ ability to classify prefrontal and postfrontal storms. Use the Sangster parameter (Column 28), the Froude height (Column 21), and the 700mb geostrophic wind speed (Column 16). Assign prefrontal storms as 1’s and postfrontal as 0’s. Use logistic regression for this analysis. Create a contingency table and contingency statistics and interpret the quality of the model.

6) Use the full predictor matrix created in 3 to formulate a hierarchical cluster analysis using Ward’s method. Provide the dendrogram. How many groups do you think there are? Interpret the results.

## Solution Preview

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prefrontal_lnd_0z <- matrix(scan('prefrontal_lnd_0z.dat'),ncol=28,byrow=T)
postfrontal_lnd_0z <- matrix(scan('postfrontal_lnd_0z.dat'),ncol=28,byrow=T)

var.names <- c("datestring","0-3_hr_verification","3-6_hr_verification","6-9_hr_verification"
,"9-12_hr_verification","0-6_hr_verification","6-12_hr_verification"
,"700_mb_geos._mag","u_bar_at_den","u_bar_at_location_"
,"500-700_mb_geostrophic_shear","700_measured/700_geostrophic_wind"
,"700_measured_-_700_geostrophic_wind","relative_humidity","cross-mountain_height_diff."
,"static_stability_ratio","froude_height","scorer_parameter","char._imped._ratio"
,"lowest_trop","local_trop","garbage_variable","postfrontal_parameter","sangster_parameter")
colnames(prefrontal_lnd_0z) <- var.names
colnames(postfrontal_lnd_0z) <- var.names...

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