Statstics

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GIS 470 Statistics for Geographers Assignment #6: Correlation and Regression

Introduction This assignment is an opportunity to showcase your knowledge of correlation and regression analysis using R. Here, we will be examining daily temperature and precipitation observations from two locations in Arizona, Phoenix and Yuma. There is a new dataset available on the Blackboard called “PhoenixYumaClimateData.csv” that you will need to download for today’s assignment. This assignment focuses on your interpretation of the R code and output rather than your ability to write new code or manipulate data. Be sure to document your work as best you can to maximize your opportunities to earn points. You are welcome to use any resources you like to complete the assignment, including the many excellent online tutorials and resources for using R. If you need to make reasonable assumptions, do so, but be sure to write out those assumptions as part of your response. The sampling distribution for all problems can be assumed to be normal.

How to complete this assignment You should upload two files to receive full credit:

1) This assignment worksheet with answers to each question typed or written by hand

2) A copy of your R code (saved as a .R file)

You are welcome to ask classmates for help, but each student should submit their own original work and code.

There are seven questions that total 100 points, plus an opportunity for a bonus point.

This assignment is due by 5pm on Monday, April 30. The assignment should be submitted electronically via Blackboard.

Good luck!

STUDENT NAME:

1. [10 points] Import the file PhoenixYumaClimateData.csv into R. Answer the following questions about the data set:

a. How many variables are in this data set?

b. How many observations are in this data set?

c. When does the period of record begin and end for these data?

d. Are there exactly the correct number of observations given the time period?

e. Are there any missing values in the data set? If so, for which variables, and how many?

2. [15 points] To get to know the data set a bit better, let’s run a series of two-tailed t-tests. We’ll compare the weather data from Phoenix to the weather data from Yuma. Before running and tests, make a few predictions:

a. Which city has higher daily maximum temperatures, on average?

b. Which city has higher daily minimum temperatures, on average?

c. Which city receives more rainfall?

d. Now let’s execute the t-tests. As you will see in the code, there are 9 different tests. Fill out the table below using output from all of the tests.

e. Average daily precipitation can be a difficult value to interpret. What is the average annual precipitation in Phoenix and Yuma?

f. Use what you have learned by running all of the t-tests to write a three-sentence summary of the major differences between the weather in Phoenix and Yuma.

3. [27 points] We used t-tests in the previous problem to draw comparisons between the data from Phoenix and Yuma. Now, we’re going to use correlation analysis to compare the two stations.

a. What will we learn from correlation analysis that we don’t necessarily learn from conducting t-tests?

b. What is the range of possible values when conducting a correlation analysis?

c. Before running any of the correlation code, make a couple of predictions.

How well correlated are daily maximum temperatures between Phoenix and Yuma? Provide a specific numerical prediction.

How well correlated is daily precipitation between Phoenix and Yuma? Provide a specific numerical prediction.

d. Run the first nine correlation tests in the code and populate the following table with the output from each.

e. In general, in which month does the weather seem to be more closely correlated between Phoenix and Yuma, December or June?

f. Let’s also explore how well correlated the daytime and nighttime temperatures are at both Phoenix and Yuma. Run the next six correlation tests and populate the following table with output from each.

g. Summarize the strength of the correlation between daily maximum and minimum temperatures at each station.

4. [5 points] Manipulating data is a very important part of any R user’s skill set. Take a look at the code in the section labeled “new function!” Run the 13 lines in this section of the code that end with plot(year, YUMA_ann_pcp). Use a combination of the plots that are generated, summary statistics, and information available in the help to describe in less than 50 words what this section of the code is designed to do. (Hint: focus on the “aggregate” function). (Hint 2: Look at the “dim” of the variables you’ve created, and see how they compare to some of the information you generated in question #1).

5. [6 points] How well correlated are the variables we created for the previous question and year? Provide a short statement for each of the six variables we’ve been analyzing.

6. [27 points] Let’s generate some linear regression models that relate year to each of the six variable’s we’ve been creating.

a. Report important output from each model in the table below.

b. In words, what is your interpretation of the slope for the temperature variables? (i.e., what does the slope “mean”)?

c. In words, what is your interpretation of the slope for the precipitation variables? (i.e., what does the slope “mean”)?

d. Provide a 2-3 sentence summary of the output of the regression models. What are the major trends we see in the variables we’ve examined over time? Were any of the trends surprising or particularly interesting to you?

7. [10 points] Assume that the historical relationship between time and each of the weather variables we’ve examined holds true into the future.

a. Fill out the table below with the model estimates for two different points in time. (Hint: remember the general form of the regression model, y=a+bx. Hint 2: You will need to write your own code to generate this output).

b. How confident are you in your predictions for 2050? Provide a short explanation regarding your level of confidence.

Congratulations for completing the sixth and final assignment for the semester!

GIS 470 Statistics for Geographers Assignment #6, page 5