Question

Select at least three variables that you believe have a linear relationship.

Specify which variable is dependent and which are independent.

Collect the data for these variables and describe your data collection technique and why it was appropriate as well as why the sample size was best.

Submit the data collected by submitting the SPSS data file with your submission.

Find the Correlation coefficient for each of the possible pairings of dependent and independent variables and describe the relationship in terms of strength and direction.

Find a linear model of the relationship between the three (or more) variables of interest.

Explain the validity of the model.

Answer 1

1. Select at least three variables that you believe have a linear relationship.

Answer:

We select the three variables cognitive skills, communication skills and sales performance that we believe has a linear relationship.

a. Specify which variable is dependent and which are independent.

Answer:

For this model, the dependent variable is given as sales performance and the independent variables are given as cognitive skills and communication skills.

2. Collect the data for these variables and describe your data collection technique and why it was appropriate as well as why the sample size was best.

Answer:

Data is collected as below:

Cognitive Skills	Communication Ability	Sales Performance $
11	19	28000
9	13	22000
8	14	21000
7	13	19000
13	17	28000
8	11	18000
9	14	22000
9	10	16000
11	20	29000
9	16	23000
8	11	14150
13	17	22250
13	17	22250
9	18	20700
13	14	19700
10	19	22150
9	19	21550
12	16	20800
9	13	16450

Data collection technique is used as the simple random sampling. About 19 sales persons are selected randomly from the list of 100 salespersons and data collected for the given three variables. The selected sample size is best for this research study because larger sample size would be expensive and time consuming.

a. Submit the data collected by submitting the SPSS data file with your submission.

Answer:

The results for regression analysis by using SPSS are given as below:

Descriptive Statistics
	Mean	Std. Deviation	N
Sales Performance $	21368.4211	3927.22727	19
Cognitive Skills	10.0000	1.97203	19
Communication Ability	15.3158	3.03777	19

Correlations
		Sales Performance $	Cognitive Skills	Communication Ability
Pearson Correlation	Sales Performance $	1.000	.504	.784
	Cognitive Skills	.504	1.000	.482
	Communication Ability	.784	.482	1.000
Sig. (1-tailed)	Sales Performance $	.	.014	.000
	Cognitive Skills	.014	.	.018
	Communication Ability	.000	.018	.
N	Sales Performance $	19	19	19
	Cognitive Skills	19	19	19
	Communication Ability	19	19	19 Variables Entered/Removedb Model Variables Entered Variables Removed Method 1 Communication Ability, Cognitive Skillsa . Enter a. All requested variables entered. b. Dependent Variable: Sales Performance $ Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .797a .635 .589 2517.46822 a. Predictors: (Constant), Communication Ability, Cognitive Skills ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1.762E8 2 8.811E7 13.902 .000a Residual 1.014E8 16 6337646.253 Total 2.776E8 18 a. Predictors: (Constant), Communication Ability, Cognitive Skills b. Dependent Variable: Sales Performance $ Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 4153.998 3532.717 1.176 .257 Cognitive Skills 326.058 343.472 .164 .949 .357 Communication Ability 911.076 222.971 .705 4.086 .001 a. Dependent Variable: Sales Performance $ 3. Find the Correlation coefficient for each of the possible pairings of dependent and independent variables and describe the relationship in terms of strength and direction. Answer: The correlation coefficients for each possible pairs are given as below: Correlations Cognitive Skills Communication Ability Sales Performance $ Cognitive Skills Pearson Correlation 1 .482* .504* Sig. (2-tailed) .037 .028 N 19 19 19 Communication Ability Pearson Correlation .482* 1 .784** Sig. (2-tailed) .037 .000 N 19 19 19 Sales Performance $ Pearson Correlation .504* .784** 1 Sig. (2-tailed) .028 .000 N 19 19 19 *. Correlation is significant at the 0.05 level (2-tailed). **. Correlation is significant at the 0.01 level (2-tailed). All correlation coefficients are significant at 5% level of significance and all correlations are positive in nature.

4. Find a linear model of the relationship between the three (or more) variables of interest.

Answer:

The regression equation for the given linear model is given as below:

Sales performance = 4153.998 + 326.058*cognitive skills + 911.076*communication skills

5. Explain the validity of the model.

Answer:

Model is valid because the p-value for this regression equation is given as 0.00 which is less than the given level of significance or alpha value 0.05. We reject the null hypothesis that the given regression model is not significant. This means we conclude that the given regression model is significant and that’s why it is valid.