TI-84 Linear Regression Instructions
A scatterplot is a graph of paired data.
Example: A company is tracking the number of visits to its website as a function of the amount of days since it launched a new product. The data is shown in the table.
Days since launch x / 2 / 8 / 15 / 22 / 35 / 40Number of website hits y / 25 / 490 / 1086 / 1622 / 2590 / 3012
Enter the data… Set up the Stat Plot…
View the Graph…
A regression fits the best equation to the scatterplot.
Choose the appropriate regression type… STAT, >, 4, V, V, V, ALPHA, TRACE, ENTER
This tells you the regression equation is
(be sure to round according to the question’s directions)
If you don’t see the r-values, go into Catalog and
select Diagnostics On, Enter, Enter.
Press GRAPH. You should see the line of best fit now, along with the scatterplot. Press TRACE and up or down to make sure the line function is selected. Now you can enter any x value to see the y value that goes with it. Type 60 ENTER.
It should show you how many website visits (y) they can expect 60 days (x) after launch. If not, adjust your WINDOW and increase xmax to a value more than 60 and ymax to 5000.
The r value tells you how strongly the data is correlated… how well x predicts y… how close to a line your scatterplot looks. Since our scatterplot lines up very nicely along a well-defined line, r is very close to 1.
r is close to ±1 : data is “strongly correlated”
r is a positive value : data has a “positive correlation” (line has a positive slope)
r is a negative value : data has a “negative correlation” (line has a negative slope)
r is close to 0 : data is not strongly correlated – doesn’t look very much like a line.
Practice: 1. Since 1990, fireworks usage nationwide has grown, as shown in the accompanying table, where t represents the number of years since 1990, and p represents the fireworks usage per year, in millions of pounds.
Years since 1990 (t) / 0 / 2 / 4 / 6 / 7 / 8 / 9 / 11Weight, y
(pounds) / 67.6 / 88.8 / 119.0 / 120.1 / 132.5 / 118.3 / 159.2 / 161.6
(a)Find the equation of the linear regression model for this set of data, where t is the independent variable. Round values to four decimal places. (b) What does the gradient (slope) represent, in the context of this problem? (c) What does the y-intercept represent? (d) Using this equation, determine in what year fireworks usage would have reached 99 million pounds. (e) Based on this model, how many millions of pounds of fireworks would be used in the year 2008? Round to the nearest tenth.
2. The accompanying table illustrates the number of movie theaters showing a popular film and the film’s weekly gross earnings, in millions of dollars.
Number of theaters x / 443 / 455 / 493 / 530 / 569 / 657 / 723Earnings y (millions) / 2.57 / 2.65 / 3.73 / 4.05 / 4.76 / 4.76 / 5.15
Write the linear regression equation for this set of data, rounding values to five decimal places. (b) What does the gradient (slope) represent, in the context of this problem? (c) What does the y-intercept represent? (d) Using the equation, find the approximate gross earnings, in millsions of dollars, generated by 610 theatres. Round your answer to two decimal places. (e) Find the minimum number of theaters that would generate at least 7.65 million dollars in gross earnings in one week.