Linear regressionDATA ANALYSIS27 SEPTEMBER 2016

Fitting a straight line through a swarm of bivariate data

Equation of a straight line

Y = a + bx

Linear regression lineY

X

(x, y)

e

a y = a + bx + e

b = y / x

Y = + X

Two hypotheses of interest… Is there no relationship between Y

and X in the population?• H0: yx = 0

Is the slope of the line = 0 in the population?• H0: = 0

Hypothesis tested about yx

Null hypothesis is H0: yx = 0

Alternate hypothesis is H1: yx ≠ 0

a = .05 Y = + X

Hypothesis tested about …Null hypothesis is H0: = 0

Alternate hypothesis is H1: ≠ 0

a = .05 Y = + X

Relationship betweencar mpg and car weight

Rscript

Console

Relationship betweencar mpg and car weight

Rscript

Console

a b

Relationship betweencar mpg and car weight

Rscript

Console

Relationship betweencar mpg and car weight

Rscript

Console

Relationship betweencar mpg and car weight

Rscript

Console

Confidence intervalsRscript

Console

Plot with regression line Rscript

Plot

Linear regressionDATA ANALYSIS27 SEPTEMBER 2016