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Chapter 4: Problem 12

Draw two scatterplots, one for which \(r=1\) and a second for which \(r=-1\).

Short Answer

Expert verified
Generated two scatterplots. The first scatterplot shows a perfect positive linear correlation with \(r=1\) which can be seen as all points fall on an upward sloping line. The second scatterplot demonstrates a perfect negative linear correlation with \(r=-1\) as all points lie along a downward sloping line.

Step by step solution

01

Create Positive Correlation Scatterplot

The easiest way to create a scatterplot with \(r=1\) is by plotting points that fall exactly on a single line. This can be done using a set of ordered pairs with an equal interval between the x and y coordinates. For simplicity, use five ordered pairs such as \((1,1)\), \((2,2)\), \((3,3)\), \((4,4)\), \((5,5)\). Plot these on the x-y graph.
02

Create Negative Correlation Scatterplot

To create a scatterplot with \(r=-1\), plot points that also fall exactly on a single line, but this time with a negative slope. It can be achieved by plotting pairs with a consistent interval between the x coordinate and a decreasing y coordinate. For simplicity, five ordered pairs such as \((1,5)\), \((2,4)\), \((3,3)\), \((4,2)\), \((5,1)\) could be used. Plot these on the x-y graph.

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Most popular questions from this chapter

In a study of the relationship between TV viewing and eating habits, a sample of 548 ethnically diverse students from Massachusetts was followed over a 19 -month period (Pediatrics [2003]: 1321-1326). For each additional hour of television viewed per day, the number of fruit and vegetable servings per day was found to decrease on average by 0.14 serving. a. For this study, what is the response variable? What is the predictor variable? b. Would the least squares regression line for predicting number of servings of fruits and vegetables using number of hours spent watching TV have a positive or negative slope? Justify your choice.

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Interest rate and number of loan applications b. Height and \(\mathrm{IQ}\) c. Height and shoe size d. Minimum daily temperature and cooling cost

For each of the following pairs of variables, indicate whether you would expect a positive correlation, a negative correlation, or a correlation close to \(0 .\) Explain your choice. a. Weight of a car and gas mileage b. Size and selling price of a house c. Height and weight d. Height and number of siblings

Briefly explain why it is important to consider the value of \(r^{2}\) in addition to the value of \(s\) when evaluating the usefulness of the least squares regression line.

A sample of automobiles traveling on a particular segment of a highway is selected. Each one travels at roughly a constant rate of speed, although speed does vary from auto to auto. Let \(x=\) speed and \(y=\) time needed to travel this segment. Would the sample correlation coefficient be closest to \(0.9,0.3,-0.3,\) or \(-0.9 ?\) Explain.
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