Name Date: Lesson 10-3: Correlation Coefficient & Making Predictions Learning Goals: #3: How do we use the line of best fit to make predictions about our data? What does it mean to extrapolate? Warm-up: 1) A craft shop sells canvasses in a variety of sizes. The table below shows the area and price of each canvas type. a. Calculate the mean point for the above data. b. Calculate the linear regression equation. Determining/Interpreting the Correlation Coefficient. Class Example Use your calculator to determine the correlation Coefficient for the data from above.
Interpreting the Correlation Coefficient Correlation Coefficient A numerical measurement used to determine the and of a relationship (Strong/Weak) (positive/negative) (*Note* Shape will always be linear because you used a linear regression) Facts about r: Making predictions Let s go back to our warm up question! A craft shop sells canvasses in a variety of sizes. The table below shows the area and price of each canvas type. a. Calculate the linear regression equation. b. Predict the amount of money it would cost to purchase a canvass that had an area of 350cm 2. How reliable are our predictions? Reliable: Unreliable: *Caution #1* We cannot use regression lines to make predictions for data values that are This is like fortune telling! We cannot predict the future! Take a look at the predictions we made in the last problem. Are they reliable? How do you know?
Putting it all together! 2) Below is a chart with the heights and weights of 10 students in a class. Student 1 2 3 4 5 6 7 8 9 10 Height x cm Weight y kg 155 161 173 150 182 165 170 185 175 145 50 75 80 46 81 79 64 92 74 108 a) Determine the equation of the line of best fit. b) What is the correlation between height and weight? What does this tell you about the relationship between height and weight? c) Predict the weight of Shaq, he is 216 cm. Give a reason why this may be unreliable. d) Predict my weight. I am 177.8 cm tall. Why is this prediction reliable?
Practice! 3) On a hot day, six cards were left in the sun for various lengths of time. The length of time each car was left in the sun was recorded, as well as the temperature inside the car at the end of the period. a) Determine the equation of the line of best fit. b) Determine the correlation coefficient. c) Based off your answer to part b, describe the relationship between time and temperature inside the car. d) Predict the temperature for a car that has been left for an hour and 20 minutes. Comment on your faith in this prediction. e) Predict the temperature for a car that has been left for 35 minutes. Comment on your faith in this prediction.
Name Date Lesson 3-3: Homework 1. Fifteen students were weighed, and their pulse rates were measured a. Create a scatter plot for the information given on the separate graph paper. b. Determine the mean, mean point, plot this point and label it M. c. Sketch a suitable line of best fit. d. Write down the correlation coefficient, and describe the relationship between weight and pulse rate. e. Determine the equation of the line of best fit. f. Use your line to predict the weight of someone who has a pulse of 72 beats per minute. Comment on your faith in this prediction.
2. Ten students were asked for their average grade at the end of their last year of high school and their average grade at the end of their last year at university. The results were put into a table as follows: a. Find the correlation coefficient r, giving your answer to two decimal places. b. Describe the correlation between the high school grades and the university grades. c. Find the equation of the regression line for y on x in the form y = ax + b. Student High School grade, University grade, y x 1 2 3 4 5 6 7 8 9 10 90 75 80 70 95 85 90 70 95 85 3.2 2.6 3.0 1.6 3.8 3.1 3.8 2.8 3.0 3.5 Total 835 30.4 d. Using this equation, predict the high school grade of a student who has a university grade of 3.4. Comment on your faith in this. e. Using this equation, predict the high school grade of a student who has a high school grade of 72. Comment on your faith in this.