Question

Question A

A. Suppose that a potential candidate for political office wishes to determine the extent to which the amount of money spent on past campaigns [X] corresponds to the percentages of popular votes that candidates receive [Y]. During the investigation, however, the potential candidate realizes that the number of weeks spent on the campaign trail [Z] may also play a role in the relationship. The candidate gathers the following data for each of these three variables from eight past political candidates:

	X	Y	Z
	[$ million]	[% popular vote]	[weeks]
	8.2	38.0	34.0
	5.2	62.0	28.0
	11.1	30.0	19.0
	6.5	61.0	39.0
	4.6	47.0	42.0
	9.7	43.0	36.0
	10.6	53.0	26.0
	6.9	72.0	38.0

[A] Find R_XY, R_XZ, and R_YZ.

[B] Calculate the multiple-correlation coefficient, R_YXZ.

[C] Explain the meaning of the results from [B] in terms of the linear relationship between money spent during campaigns, weeks spent campaigning, and percentage of popular vote.

Question B

B. Find the coefficient of multiple determination for the data presented in Question A.. What does this value indicate?

Answer 1

A) Rxy, Rxz, and Ryz can easily be calculated using excel:

Step 1: Put the data into the excel spreadsheet

Step2:Go to data --> data analysis --> correlation

Step 3: To calculate rxy, select data of the first two columns and click ok

Rxy = -0.5521

Step 4: To calculate rxz, select data of the first and third column and click ok

Rxz = -0.6592

Step 5: To calculate ryz, select data of the first and third column and click ok

Ryz = 0.4187

b) Multiple Correlation Coefficient:

Following formula can be used to calculate the Rxyz

C) Interpretation of Ryxz

The value of Ryxz = 0.5569 indicates that there is a moderately positive relationship between the dependent and independent variables. The money spent on campaigning is moderately related to the week spent campaigning and the percentage of the popular vote.

d)Coefficient of multiple determination

The coefficient of multiple determination can be calculated as the square of Multiple correlation coefficient

The value of multiple determination of 0.3101 indicates that 31% of the variation in dependent variable is explained by the independent variables.