 Recall: A line of best fit is drawn through a set of data points to best represent a linear relationship between 2 variables  Line of best fit is aka Regression Line or Trend Line  Line needs to be closest to each point – the more varied the position of the points, the harder to draw the line of best fit

 Observing a relationship between two variables does not mean that one variable causes a change in the other  Other factors could be involved, or the correlation could be a coincidence In this case, it’s not a coincidence than pain accompanies a needle!

Open window (A) and fly kite (B). String (C) lifts small door (D) allowing moths (E) to escape and eat red flannel shirt (F). As weight of shirt becomes less, shoe (G) steps on switch (H) which heats electric iron (I) and burns hole in pants (J). Smoke (K) enters hole in tree (L), smoking out opossum (M) which jumps into basket (N), pulling rope (O) and lifting cage (P), allowing woodpecker (Q) to chew wood from pencil (R), exposing lead. Emergency knife (S) is always handy in case opossum or the woodpecker gets sick and can't work.

 State whether the claim in each situation is reasonable:  A) A scientific study showed a negative correlation between aerobic exercise and blood pressure. It claimed that the increase in aerobic activity was the cause of the decrease in blood pressure.

 A) It is reasonable to think there may be a cause and effect relationship. There are many factors that affect blood pressure however. Since this is a scientific study, we might reasonably expect that the researchers made efforts to neutralize other factors, for example, by studying subjects in a very close age and fitness range.

 B) Mila discovered a positive correlation between gasoline price and average monthly temperature. She concluded that temperature determines the price of gasoline.

 B) It is not reasonable to say there is a cause- and-effect relationship between temperature and gasoline prices. A more likely explanation for the correlation is that higher temperatures occur in the summer, when more people are travelling out of town for weekends and vacations. This increased demand could cause the price increase.

 Since the 1950s, the concentration of carbon dioxide in the atmosphere has been increasing. Crime rates in many countries have also increased over this time period. Does more carbon dioxide in the atmosphere cause people to commit crimes?

 C) It is not reasonable to say there is a cause-and-effect relationship. It is much more likely that carbon dioxide levels and crime rates are each determined by many other factors, such as increasing populations.

Below are pre-exam term marks and exam marks for some students in a Grade 12 math course. a) Graph the data and draw the line of best fit. b) Determine the equation of the line of best fit. c) Use the data to predict the exam mark of a student with a pre-exam term mark of 98% d) Use the data to predict the exam mark of a student with a pre-exam term mark of 10%

(a)

Equation of a Straight Line y = mx + b 80 = (0.96)(80) + b 80 = b b = 80 – 76.8 b = 3.2 y = 0.96x (b)

Pre-exam term mark: 98% Exam Mark: y = 0.96x when x=98 y = 0.96(98) = = or 97% (c) Pre-exam term mark: 10% Exam Mark: y = 0.96x when x=10 y = 0.96(10) = = 12.8 or 13% (d)

 p. 186 #1, 2, 3, 4, 6, 7