Correlation and linear regression


correlation, scatter plot, regression line

At the bottom of that webpage, at
**************************************
Exercise data
are sets of X Y paired data at r ≈ 0, .2, .3, .5, .7, .9
of same size n, same means and SDs

Copy and paste the X and Y data into their respective input areas.
r ≈ 0
n r r2 p-value Reject H0
α=.05 ? 		Reject H0
α=.01 ? 		r critical value
α=.05 		r critical value
α=.01 		slope of
regression line 		Σresiduals2 SD residuals Prediction.
x0=100

Reject H0?
Reject H0? 		ŷ=
95% CL E=
99% CL E= 
What percent of the Ys are "explained" by the Xs:____

Conclusion: the population parameter ρ __ 0, there is___ or is not___ a correlation in the population.
r ≈ .24
n r r2 p-value Reject H0
α=.05 ? 		Reject H0
α=.01 ? 		r critical value
α=.05 		r critical value
α=.01 		slope of
regression line 		Σresiduals2 SD residuals Prediction.
x0=100

Reject H0?
Reject H0? 		ŷ=
95% CL E=
99% CL E= 
What percent of the Ys are "explained" by the Xs:____

Conclusion: the population parameter ρ __ 0, there is___ or is not___ a correlation in the population.
r ≈ 5.
n r r2 p-value Reject H0
α=.05 ? 		Reject H0
α=.01 ? 		r critical value
α=.05 		r critical value
α=.01 		slope of
regression line 		Σresiduals2 SD residuals Prediction.
x0=100

Reject H0?
Reject H0? 		ŷ=
95% CL E=
99% CL E= 
What percent of the Ys are "explained" by the Xs:____

Conclusion: the population parameter ρ __ 0, there is___ or is not___ a correlation in the population.
r ≈ .9
n r r2 p-value Reject H0
α=.05 ? 		Reject H0
α=.01 ? 		r critical value
α=.05 		r critical value
α=.01 		slope of
regression line 		Σresiduals2 SD residuals Prediction.
x0=100

Reject H0?
Reject H0? 		ŷ=
95% CL E=
99% CL E= 
What percent of the Ys are "explained" by the Xs:____

Conclusion: the population parameter ρ __ 0, there is___ or is not___ a correlation in the population.
Summary: As r increases, r2 ________, slope _______, sum of squared residuals ________, SD of residuals _______, p-value ______, prediction E ___________

effect of n?

negative r example?