Practice Quiz with Solutions: Chapter 4

Disclaimer: This quiz is representative of the level of difficulty you should expect, but it doesn’t include every single topic from the week’s work. The real quiz may include some other topics and may skip some that are in this practice quiz. (The real quiz also may not word questions in the same way as the practice quiz. You should focus on the concepts, not a particular form of words.)

These solutions show about the same level of work I expect from you, though I add quite a bit of extra commentary. Please see Show Your Work for the what, why, and how.

1(points: 2) An Internet provider charges for bandwidth according to the equation y = 35.00 + 0.005x where x is the traffic in megabytes and y is the charge in dollars. What is the mathematical term for the number “0.005” in this equation?

Remark: Some students answer in paragraphs. Short answers are best: they save you time writing and they save me time scoring. For this question, the one word “slope” was a fine answer.

For a random sample of TC3 students, the number of hours of TV per day and the GPA were recorded. Results were as follows:

TV hr/day, x	1	8	3	2	6	1	3	7	4	9
GPA, y	3.2	2.7	3.1	3.7	2.9	3.0	2.9	2.5	3.0	2.6

(a) (points: 6) Find the correlation coefficient regression output screen and the equation of the line that fits these points best. Round to four decimal places, and label them with their proper symbols.

Solution: Look at the scatter plot (not shown here) and see that the y’s tend downward as x’s tend to the right; therefore you expect r and the slope of the regression line to be negative. (If you need to, review the methods explained in Scatter Plot, Correlation, and Regression on the TI-83/84.)

        x’s in L1
        y’s in L2
        LinReg(ax+b) L1,L2,Y1

r = −0.7547

ŷ = −0.0882x + 3.3482

Common mistake: Many students tend to forget those little minus signs. They’re not just decoration! Always look at the scatter plot before performing the regression, and ask yourself whether you expect a positive or negative correlation and slope.

(b) (points: 3) Based on the regression, what is the expected GPA (accurate to two decimal places) for a student who watches 7 hours of TV daily? Use the proper symbol in your answer. regression line with trace for x=7

Solution: Using Trace, enter x = 7 and read off ŷ = 2.7306283 → 2.73

Common mistake: The answer 2.5 is incorrect; that’s just one data point. A different student watching 7 hours a day would probably have a different GPA. The point of a regression is to predict the average GPA of students who watch 7 hours a day.

Common mistake: Make sure you know the difference between y and ŷ.

Alternative solution: You could substitute 7 in the regression equation:

ŷ = –0.0882(7) + 3.3482

ŷ = 2.7308 → 2.73

In this particular case the rounded answer is correct, but it’s always dangerous to use rounded coefficients. Never round a calculation in the middle! For safety, either use the complete numbers (−0.0882198953 and 3.348167539) or use the much easier tracing method.

(c) The decision point for sample size 10 is 0.632. What if anything can you conclude about the relation between TV watching and GPA for all TC3 students?

Answer: r is negative and |r| = 0.7547 is larger than the decision point; therefore there’s a negative association between TV watching and GPA.

Answer: As x increases, y does not consistently increase or decrease. Therefore r is near zero.

(You could also say that the points obviously don’t fit any straight line, and therefore the linear correlation is near zero.)

Remark: Although the points obviously don’t fit a straight line, it’s equally obvious that there’s some connection between the variables. Since the points look like they fit a parabola, if this were a real-life situation you would try quadratic regression on your TI-83.

4(points: 2) You perform a regression and your calculator returns a value of r² = 0.2. What does that tell you about the regression?

Answer: Only 20% of the variation in y is associated with variation in x. The line of best fit does not fit the points very well, and the predictions you obtain from it won’t be very good. Either the measurements have a lot of error in them, or other factors are more important than this particular x variable.

Practice Quiz with Solutions: Chapter 4 (20 min)