Aim #93: How do we distinguish between scatter plots that model a linear versus a nonlinear equation and how do we write the linear regression equation for a set of data using our calculator? Homework: Handout Do Now: 1) A scatter plot is an informative way to display numerical data with two variables. Here is a scatter plot of the data on elevation and mean number of clear days. a) Do you see a pattern in the scatter plot, or does it look like the data points are scattered? b) How would you describe the relationship between elevation and mean number of clear days for these 14 cities? Do the mean number of clear days tend to increase or decrease as elevation increases? Since the points correlate in a linear fashion, a linear regression equation (also known as the line of best fit or least squares line) can be used to represent the relationship between the mean number of clear days and elevation. The line of best fit will not go through every point on this scatter plot above. 2) The scatter plot below shows number of cell phone calls and age. Is there a relationship between number of cell phone calls and age? If there is a relationship between number of cell phone calls and age, does the relationship appear to be linear?
3) Below are three scatter plots. Each one represents a data set with eight observations. The scales on the x and y axes have been left off these plots on purpose so you will have to think carefully about the relationships. a) If one of these scatter plots represents the relationship between height and weight for eight adults, which scatter plot do you think it is and why? b) If one of these scatter plots represents the relationship between height and SAT math score for eight high school seniors, which scatter plot do you think it is and why? c) If one of these scatter plots represents the relationship between the weight of a car and fuel efficiency for eight cars, which scatter plot do you think it is and why? d) Which of these three scatter plots does not appear to represent a linear relationship? Explain the reasoning behind your choice.
4) Describe the type of relationship (linear, exponential, quadratic, or none) for each scatter plot: 5) The scatter plot below compares frying time and moisture content. Is there a relationship, and if so, what type, between these variables or do the data points look scattered?
6) The scatter plot below shows a straight line that can be used to model the relationship between elevation and mean number of clear days. The equation of this line is y = 83.6 + 0.008x. a) There are 14 US cities shown in the scatter plot above. Should you see more clear days per year in Los Angeles, which is near sea level or in Denver which is known as the mile high city? Justify your choice. b) One of the cities in the data set was Albany, New York, which has an elevation of 275 feet. What would you predict this number to be based on the equation of the line that describes the relationship between elevation and mean number of clear days? c) Another city in the data set was Albuquerque, New Mexico. It has an elevation of 5,311 feet. What would you predict this number to be using the equation of the line? d) The actual value for Albany is 69 clear days and the actual value for Albuquerque is 167 clear days. Was the prediction of the mean number of clear days based on the line closer to the actual value for Albany or for Albuquerque? How could you tell this from looking at the scatter plot with the line shown above?
7) Kendra watched a show where investigators used a shoe print to help identify a suspect in a case. She questioned how it is possible to predict someone s height from his shoe print. To investigate, she collected data on shoe length (in inches) and height (in inches) from 10 adult men. Her data appears in the table and scatter plot below. Steps for finding the linear regression equation (also known as the line of best fit) 1. Stat Edit Enter your data into L1 and L2 2. Stat Calc Choose LinReg (4) a) Using your calculator, write the linear regression equation for the table above where shoe size is the independent variable. Round the slope to the nearest hundredth and y-intercept to the nearest tenth. b) Is there a relationship between shoe length and height? Explain c) Do the men with longer shoe lengths tend to be taller? d) Using the equation of the line of best fit from part (a), predict the height of a man with a shoe length of 12 inches. Round to the nearest hundredth. e) Use the equation of the line of best fit to predict the height of a man with a shoe length of 12.6 inches. f) How does the predication from part e compare to the first data point in the table? Sum it up! A scatter plot can be used to investigate whether or not there is a relationship between two numerical variables. This relationship can be described as linear or nonlinear.