Baseball – Linear Regression t-test and confidence intervals



Name ____________________due 3/21/18

1. Give your calculator a random starting place by entering your ID # into RAND.

(# STO MATH PRB 1 Enter). Then from the list of years, choose a random sample of 9 years. Use randint(1917,2017,9) in the Math PRB menu. If you get a duplicate, generate another random integer. Write the year and the total days since earliest break-up. (Use two-decimal places.) Put the data into L1 and L2 in your calculator.

Year | | | | | | | | | | |Total Days | | | | | | | | | | |

2. Using the year and total days, create a scatterplot. (Label and number axes) Do not just draw what you see in your calculator – be accurate.

3. Describe the relationship between year and break-up day.

4. Find the least squares regression equation. (STAT CALC 4). Don’t forget to define the variables.

5. Complete the interpretation of the slope of the equation.

For every additional year that passes,

6. Why is it not reasonable to interpret the y-intercept?

7. Give the value of the correlation coefficient r . (If this did not show when you did the linear equation go to 2nd 0 (Catalog) and turn on the diagnostics (DiagnosticOn Enter Enter)) What does this tell us about the strength and direction of a possible linear relationship?

8. Give the value of the coefficient of determination R-square. Interpret this value in context. Hint: helps explain variability in y

9. Recall that after each regression calculation, the calculator saves the residuals in a list called RESID. (2nd STAT NAMES) You may want to put them in List 3 to see them clearly. Do a plot of the residuals vs the x- values. (Label and number the axes)

10. What does your residual plot tell you about the adequacy of your linear model? (With only a few points, sometimes it is hard to be sure about seeing a pattern or lack of)

11. Using your linear model, what is your prediction for when the ice will break in 2018? Record that number below. Record that number on a WU sheet. Also enter a guess of your own, determine a date, hour, and minutes for the break –up and record it on the large paper for your class. Turn in BOTH numbers on ONE small paper. A prize will be awarded for the person who gets closest to the actual date and time.

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