Reexamine the women's optimism score data we used in Week 2's Discussion Board (the excel file is named "Week2DiscussionQuestion1Data" and is also attached below). Using this data set again, perform a correlation analysis using the age ("age") as a predictor of the Optimism Score ("Optimism Score") of all subjects.

• Week2DiscussionQuestion1Data- Excel Document (52 KB)

2. Plot the data with a regression line and perform a regression with the appropriate statistical test in StatCrunch. Copy and paste your graph and regression output into your Word for posting.

Simple linear regression results:

Dependent Variable: Optimism Score

Independent Variable: Age

Optimism Score = 54.264144 - 0.26550274 Age

Sample size: 1000

R (correlation coefficient) = -0.157605

R-sq = 0.024839337

Estimate of error standard deviation: 10.33807

Parameter estimates:

Parameter

Estimate

Std. Err.

Alternative

DF

T-Stat

P-value

Intercept

54.264144

1.9573379

0

998

27.723442

<0.0001

Slope

-0.26550274

0.052658904

0

998

-5.0419344

<0.0001

Analysis of variance table for regression model:

Source

DF

SS

MS

F-stat

P-value

Model

1

2716.898

2716.898

25.421102

<0.0001

Error

998

106661.95

106.8757

Total

999

109378.84

1. What is the correlation coefficientrand what is the coefficient of determination here? What does the coefficient of determination mean in this case?

1. Is there a statistically significant correlation between age and optimism in this sample?
2. What hypotheses did you test?

1. Using StatCrunch (be sure to copy and paste your predicted Y output from StatCrunch into your submission), what is the predicted optimism score for someone aged 45?