Writers Den

PSY 870: Module 7 Problem Set

Optimism
and Longevity

A cancer
specialist from the Los Angeles County General Hospital (LACGH) rated patient
optimism in 20- to 40-year-old male patients with incurable cancer in 1970. In
1990, the researcher examined hospital records to gather the following data:

·
Socioeconomic status (1–7
rating of occupation; higher ratings indicate higher levels of SES)

·
Age in 1970

·
Optimism in 1970 (1–100 rating,
higher scores indicate higher levels of optimism)

·
Longevity (years lived after
the 1970 diagnosis)

Using the
SPSS data file for Module 7 (located in Topic Materials), calculate a
simultaneous multiple regression with SES, age, and optimism as the independent
variables and longevity as the dependent variable.

1.
Do the independent variables
correlate statistically significantly and practically with the dependent
variable?

The obtained correlation coefficient output is given below,

Correlations
	Age	Socioeconomic Status	Optimism	Years Lived after Diagnosis
Age	Pearson Correlation	1	-.290**	-.431**	-.332**
Sig. (2-tailed)		.000	.000	.000
N	244	244	244	244
Socioeconomic Status	Pearson Correlation	-.290**	1	.520**	.369**
Sig. (2-tailed)	.000		.000	.000
N	244	244	244	244
Optimism	Pearson Correlation	-.431**	.520**	1	.573**
Sig. (2-tailed)	.000	.000		.000
N	244	244	244	244
Years Lived after Diagnosis	Pearson Correlation	-.332**	.369**	.573**	1
Sig. (2-tailed)	.000	.000	.000
N	244	244	244	244
**. Correlation is significant at the 0.01 level (2-tailed).

Here we can see that all the correlation coefficients are
significant at 0.01 significant level thus independent variables correlate
statistically significantly and practically with the dependent variable.

2.
Is collinearity between the
independent variables a concern?

As the correlation coefficient between the independent variables are
significant so yes collinearity between the independent variables is a concern.

3.
What is theRand
adjustedR-square for all independent variables entered simultaneously?

The obtained output is given below,

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.585a	.343	.334	3.647
a. Predictors: (Constant), Optimism, Age, Socioeconomic Status

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	1663.187	3	554.396	41.684	.000b
Residual	3192.026	240	13.300
Total	4855.213	243
a. Dependent Variable: Years Lived after Diagnosis
b. Predictors: (Constant), Optimism, Age, Socioeconomic Status

Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.
B	Std. Error	Beta
1	(Constant)	3.773	2.131		1.770	.078
Age	-.073	.044	-.097	-1.675	.095
Socioeconomic Status	.236	.164	.089	1.441	.151
Optimism	.175	.023	.485	7.433	.000
a. Dependent Variable: Years Lived after Diagnosis

From the output we can see that the required R-sq are adjusted R-sq
are 0.343 and 0.334 respectively.

4.
What variable(s) provide a
significant unique contribution(s)?

The p-value for Optimism is smaller than the significance level of
0.05 so only this variable provides a significant unique contribution.

5.
Compose a results section for
this statistical analysis.

We saw that the multicollinearity is an issue
which we have to deal with. Also out of 3 variables only 1 plays important role
in prediction so we might need to transform the variables to some level so see
whether they comes significant or not.