Math 503

Lab: Data Collection

I. Circle: Imagine you don=t know that the circumference of a circle is equal to 2π r.

We want to discover a relationship between the circumference of a circle and its radius. Find some round things, measure the circumference and radius of each. To do this work in groups of two. You should use at least 10 round objects with varying sizes. Each person should measure each object at least once alternating who measures first and keeping track which measurement belongs to which person.

Enter these data into Minitab using 3 Columns: Circumference, Radius, Person.

Scatter plot the data.

Do you see a relationship between Circumference and Radius?

If you so, what might your data suggest is a formula for the relationship?

II. . Pendulum: The time it takes for a pendulum to make a full swing back and forth seems to somehow depend on the length of the pendulum. Make 10 pendulums of varying lengths. Measure the time it takes for the pendulum to make 5 swings. One person should hold the pendulum and the other time it. Then switch jobs and do this again.

Enter these data into Minitab using 3 Columns: Length, Time, Person.

Scatter plot the data.

Do you see a relationship between Length and Time?

If you so, what might your data suggest is a formula for the relationship?

III. Reload your circle data. You know that the relationship between circumference and radius is linear. Use Minitab=s correlation and regression analyses to examine the relationship. Use the R² and the residuals to justify this relationship.

A.Calculate correlation coefficient

Use Stat 6 Basic Statistics 6 Correlation

Enter X and Y* as variables

Click OK

B. Run regression analysis and fit line to the data.

Use Stat 6 Regression 6 Fitted Line Plot

Enter Y* for response and X for predictor

Click OK

Note the values of the coefficients of the constant (a) and the x (b). Also note values of R-sq, s, t, F, and p in addition to the correlation coefficient, and the graph.

C. Plot the Standardized Residuals ( A standardized residual is a standardized difference between the actual value of y and the value predicted by Minitab's values of a and b; i.e. r = y - (a + bx) and a standardized residual is r/s where s is an estimate of the variance of the residuals.) The residuals should have a normal distribution and be scatter randomly about the horizontal axis, IF we have a good fit to our data. To do this:

Use Stat 6 Regression 6 Regression

Enter Y for response and X for predictor

Click on Graphs

Select Standardized, Normal Plots of Residuals, and Residuals vs fits.

Click OK; Click OK

IV. You actually know that the relationship between circumference and radius is linear with the y intercept equal to 0. Redo part I and tell Minitab to fit the line through the origin; i.e. that the intercept is 0. To do this uncheck the box fit intercept in the options for regression.

V. Use regression to fit a straight line to your pendulum data. This fit probably won=t be good C justify this using residual analysis.

(Repeat parts A-C above)