Linear Regression Homework

Public debt increased at nearly a constant rate from 1986 to 1996. The table at the right gives the average debt per capita, in thousands of dollars, for selected years.

1. Use a graphics calculator to determine a linear regression model for the data (use the second and third columns).
2. Use the model to estimate the per capita debt in 1995.
3. Use the model to estimate when the per capita debt was $14,000 per capita.
4. Interpret the slope of your model. (Explain in words what the slope means.)

On January 1, 1998, the I.T.&T. Company instituted a factory safety program. This was a comprehensive safety program which included education of employees and installation of new (safer) equipment. The table at the right shows the number of days of work missed during the month, due to workplace injuries, (for each of the first 6 months of 1998) as a function of the month (t=1 means January 1998; t=4 means April 1998).

1. Use a graphics calculator to determine a linear regression model for the data.
2. Use the model to estimate the number of work days missed in August.
3. Use the model to estimate when the number of work days missed will reach 120 days.
4. Interpret the slope of your model. (Explain in words what the slope means.)
5. Interpret the vertical intercept (y-intercept) of your model.

A scientist collected the following data on the speed, in cm per second, at which ants ran at the given ambient temperature, in degrees Celsius.

1. Use a graphics calculator to determine a linear regression model for the data.
2. Use the model to estimate the speed if the temperature is 31 degrees Celsius.
3. If the ants are running at a speed of 3.25 cm/sec, what's the temperature?
4. Interpret the slope of your model. (Explain in words what the slope means.)
5. The vertical intercept (y-intercept) of your model should be a negative number! Explain why this doesn't make sense. That is, why the vertical intercept does not give us useable information. (The model has limitations.)