Question

Sales of cars since 2010 have increased fairly linearly. View the table below and answer the following questions. Using your calculator, find the equation for the line of best fit to model the data. Extrapolate the data by making a prediction of how many cars will be sold in the year 2025 (15 years since 2010). Using your calculator, find the correlation coefficient for the line of best fit. What does this value tell you about the relationship between years passed since 2010 and the number of car sales?

Answer 1

To find the equation for the line of best fit, you can use the method of least squares. This involves finding the equation of a line that minimizes the sum of the squared differences between the actual data points and the predicted values on the line. To do this, you would first need to input the data points into your calculator. Then, using the linear regression function on your calculator, you can find the equation for the line of best fit. This equation will have the form y = mx + b, where m is the slope of the line and b is the y-intercept. Once you have the equation, you can use it to make a prediction for the number of cars sold in the year 2025, which is 15 years since 2010. Simply substitute the value of x as 15 into the equation and solve for y. This will give you the predicted number of cars sold in 2025. To find the correlation coefficient for the line of best fit, you can use the correlation function on your calculator. The correlation coefficient, denoted by r, measures the strength and direction of the linear relationship between the years passed since 2010 and the number of car sales. The correlation coefficient ranges from -1 to 1. A positive value of r indicates a positive linear relationship, meaning as the years passed since 2010 increase, the number of car sales also tends to increase. A negative value of r indicates a negative linear relationship, meaning as the years passed since 2010 increase, the number of car sales tends to decrease. The closer the value of r is to 1 or -1, the stronger the linear relationship. A value close to 0 indicates a weak or no linear relationship. In summary, to find the equation for the line of best fit, input the data points into your calculator and use the linear regression function. To make a prediction for the number of cars sold in 2025, substitute the value of x as 15 into the equation and solve for y. To find the correlation coefficient, use the correlation function on your calculator. The correlation coefficient tells you about the strength and direction of the linear relationship between the years passed since 2010 and the number of car sales.