linear regression

line of best fit

(r)(sy)/(sx)

y-intercept

mean of y-(slope(mean of x))

residuals

observed-predicted

conditions for linear models

1) random samples and independent observations
2) values of y variable are normally distributed around each x
3) straight enough condition: the scatterplot confirms that there is an approximately linear relationship
4)no influential outliers
5)do the points remain fairly consistently spread around the line (does the plot thicken)

residual plots

help visually determine if our data meets the conditions
-show the x values on the x-axis and residual values on the y-axis

no violations

even scatter

funneling shape

violates same variance (does the plot thicken)

linearity

if there's a curve in the residual graph then there's a violation. Should not be able to see any patterns

Assessing fit

square r
-shows how much of dependent variable is explained by independent variable

r squared values

greater than .8 is ideal

how to calculate R squared

1-((SS residuals)/(SStotal))

test of significance

is our slope a significant predictor in the population, can use a t-test on our slop estimate.

null hypothesis

slope equals 0

alternate hypothesis

slope does not equal 0

t-stat

t=(slope-0)/sb

when rejecting the null

there is a relationship between the two variables

what to include in a regression conclusion

1) Model
2) interpret y-int
3) state slope
4)test of significance
5) what are the assumptions
6) R squaredsl

slope value of the null

is always zero

example of slope interpretation
height=52.90+1.47shoesize

as we increase by 1 shoesize the predicted height increases by 1.47 in.

example of y-int interpretation
height=52.90+1.47shoesize

a 0 shoe size person is predicted to be 52.9 in. tall