Reference no: EM132263686

Quantitative Research Methods In Geography Assignment - Correlation And Regression

INTRODUCTION - The purpose of this assignment is to familiarize students with the procedure and interpretation of goodness of fit, as well as correlation and regression.

ASSIGNMENT -

SECTION I - Goodness of Fit Test

The City of Winnipeg is interested in knowing if the nationality of foreign tourists is related to which tourist attraction they liked most. The observed frequencies of tourists visiting four tourist attractions in the city are provided below.

Research Question: The municipal government assumes that the number of tourists from the various countries visiting tourist attractions in Winnipeg is random.

Complete this question using the critical value method discussed in class (you will not be using SPSS to find the answer).

Question 1: Which hypothesis test would you use to investigate the problem? Justify your answer.

Question 2: Summarize and compare the results from the test. In your answer,

i. State your null hypothesis and alternative hypothesis.

ii. Specify your significance level.

iii. Provide the calculations you performed.

iv. State whether the null hypothesis should be rejected or accepted based on critical and test statistic and explain why.

v. Finally conclude regarding the research question.

Question 3: What would you advise the City of Winnipeg? Why?

SECTION II - TESTING FOR NORMALITY

Select one continent (Asia, Africa or Latin America) from assignment 5 and test whether the per capita GNP for the countries is normal or not. This is done using the following method in SPSS:

• Select ANALYZE > DESCRIPTIVE STATISTICS > EXPLORE.
• Select the Test Variable (the column with the sample values) and move it into the Dependent List. Highlight the variable in the column on the right and click the top arrow (beside Dependent List).
• Click PLOTS on the right. A new window pops out. Check None for boxplot, uncheck everything for descriptive and make sure the box NORMALITY PLOTS WITH TESTS is checked.
• Select OK. The third table has the test statistics required to draw the conclusion. Use the Shapiro-Wilk information.

Question 1: Summarize and compare the results from the test. In your answer,

i. State your null hypothesis and alternative hypothesis.

ii. Specify your significance level and critical statistic.

iii. Attach the test results from SPSS.

iv. State whether the null hypothesis should be rejected or accepted based on p-value and test statistic and explain why.

v. Finally conclude regarding the research question.

Section III - Correlation and Regression

In this correlation/regression exercise, you have been hired to investigate the association and relationship between the number of private dwellings and the population of various cities in Canada. The Canada Mortgage and Housing Canada needs to know if they should invest more money in housing within the larger cities or the smaller cities. The data is found in UMLearn (private dwellings.xls).

Research Question: Is there an association and relationship between the number of private dwellings and the population in 2016.

TASK 1: CREATE A SCATTERPLOT

Using the graphing method described in a previous assignment, produce a simple scatterplot of the number of private dwellings and population. You should be careful in the selection of the independent and dependent variables. These should be based on the question in the paragraph above. Edit the plot to include the name of the variables you are using. Information on how to do a boxplot can be found in a previous assignment.

Question 1: Include a copy of your scatterplot in your assignment report. Your grade will be in part based on whether the axes are labelled.

Question 2: On the basis of the scatterplot, do you expect a statistically significant association between the two variables? Justify your answer. If so, do you expect a positive or negative association and why?

TASK 2: CORRELATION ANALYSIS

To compute the Pearson's correlation coefficient associated with the data in this question in SPSS do the following.

• Select ANALYZE > CORRELATE > BIVARIATE
• Select the two variables you want to compare. Highlight them in the variable list and move to the Variables box. Make sure PEARSON is checked.
• Specify whether the test of significance should be one-tailed or two-tailed.
• Select OK.

To compute the Spearman's correlation coefficient associated with the data in this question in SPSS do the following. Do the correlations for both years at the same time.

• Select ANALYZE > CORRELATE > BIVARIATE
• Select the two variables you want to compare. Highlight them in the variable list and move to the Variables box. Make sure SPEARMAN is checked.
• Specify whether the test of significance should be one-tailed or two-tailed.
• Select OK.

Question 3: Which is most appropriate for this question - the Pearson's or Spearman's correlation? Briefly justify your answer?

Based on the correlation method you selected for Question 3, answer the following questions:

Question 4: Provide the correlation table for either the Pearson or Spearman correlation analysis you just completed.

Question 5: What are the correlation coefficient and p-value for these results? Provide only one set of values.

Question 6: What do these values indicate about the strength and direction of the association between the two variables?

TASK 3: REGRESSION ANALYSIS

Assume the correlation coefficient indicate that a regression model should be produced between these variables. Test the hypothesis that 'there is evidence that the population positively or negatively affects the number of private dwellings in Canada'.

To run a regression analysis in SPSS for the data:

• Select ANALYZE > REGRESSION > LINEAR
• The linear regression dialog box will appear. You will need to specify the dependent and independent variables.
• You can experiment with the Statistics and Plot boxes found at the bottom of the dialog box. This is not necessary.
• Select OK.

Question 7: Which is the independent and which is the dependent variable? Justify your choice.

Question 8: Provide the regression tables.

Question 9: How much of the variation in the dependent variable does the variation in the independent variable explain? Which statistic in the table provides this answer? Explain.

Question 10: What is the line of best fit that represents your model? Is this model statistically significant? Which statistic in the table provides this answer?

Question 11: Does this relationship mean that the independent variable you selected has a direct impact on the dependent variable? Why or why not?

Attachment:- Assignment File.rar