STAT1008 Lecture Notes - Lecture 31: Observational Error, Scatter Plot, Confidence Interval
STAT1008 Week 11 Lecture A
● Slope and Intercept
○ The estimated regression line is: y = a + bx
○ Slope: increase in predicted y for every unit increase in (b)
○ Intercept: predicted y value when x = 0 (a)
● Interpreting slope and intercept:
○ Slope = 0.23
■ The predicted temperature goes up by about 0.23OF for every increase of
one in the chirp rate
○ Intercept = 37.7:
■ The predicted temperature when crickets stop chirping?
● Units
○ It is helpful to think about units when interpreting a regression equation
■ y = a+b.x
○ Intercept matches response variable but explanatory is different and slope is a
combination of both x and y units
○ E.g. Temp and chirping data
■ The 37.7 is also in degrees and 0.23 is both degrees and chirps per
minute
○ Change the unit of measurement => change in equation
○ What is we standardise the explanatory variable?
■ 68.36 + 10.11zchirps where zchirps = (chirps-mu)/sigma for the example
○ As you change the response or explanatory variable the intercept or slope will
change
● Regression caution 1:
○ Don’t use the regression equation or line to predict outside the range of x values
available in your data (don’t extrapolate!)
○ If none of the x values are anywhere near 0, then the intercept is meaningless!
● Regression caution 2:
○ Computers will calculate a regression line for any two quantitative variables, even
if they are not associated or if the association is not linear
● Regression caution 3:
○ Outliers (especially outliers in both variables) can be very influential on the
regression line
○ ALWAYS PLOT YOUR DATA!
○ Life expectancy and birth rate
■ Which of the following interpretations is correct? Intercept = 83.4090 and
Life Expectancy = -0.8895
● Answer = neither
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
The estimated regression line is: y = a + bx. Slope: increase in predicted y for every unit increase in (b) Intercept: predicted y value when x = 0 (a) The predicted temperature goes up by about 0. 23of for every increase of. It is helpful to think about units when interpreting a regression equation. Intercept matches response variable but explanatory is different and slope is a combination of both x and y units. The 37. 7 is also in degrees and 0. 23 is both degrees and chirps per minute. Change the unit of measurement => change in equation. 68. 36 + 10. 11zchirps where zchirps = (chirps-mu)/sigma for the example. As you change the response or explanatory variable the intercept or slope will change. Don"t use the regression equation or line to predict outside the range of x values available in your data (don"t extrapolate!) If none of the x values are anywhere near 0, then the intercept is meaningless!
