scatter plots, linear relationships, least squares regression

Question 1

association between quantitative variables

Answer 1

can be seen using a scatterplot - how the change in one variable affects another

positive association: above average values of one variable tend to occur with above average values of the second variable (same with below average values) - slope is positive

Question 2

scatterplot

Answer 2

if there is an explanatory variable, it goes on the horizontal axis. response variable on the vertical axis

Question 3

forms of scatterplots

Answer 3

linear, curves, clusters

Question 4

direction of scatterplots

Answer 4

positive or negative association

Question 5

strength of association

Answer 5

how close the points lie in the simple form of a straight line

Question 6

fitting straight lines - method of least squares

Answer 6

need to determine what lines are closest to the points

• a regression line describes how the response variable changes in response to the explanatory variable - Canberra used to predict y from x values
• vertical displacement of the line are errors or residuals
• error observed for xi, yi is (data value - predicted value)
• the line that minimised the sum if squared error is the line of best fit or regression - sum of squares is zero is the perfect line