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Chapter 3: Q 60. (page 193)

Oil and residuals Refer to Exercise 59. The following figure shows a residual plot for the least-squares regression line. Discuss what the residual plot tells

Short Answer

Expert verified

The regression line is not a good fit for the data.

Step by step solution

01

Part (a) Step 1: Given information

02

Part (a) Step 2: Concept

A regression line is a straight line that depicts the change in a response variable y when an explanatory variable x changes. By putting this x into the equation of the line, you may use a regression line to predict the value of y for any value of x

03

Explanation

The anticipated laboratory value from the least-squares line is within -20and +20for the majority of the residuals in the exhibited image. As the laboratory measurement (X)grows, the residual plot shows an increasing spread around the regression line. For larger values of Xpredictions of Yusing this line will be less accurate.

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Most popular questions from this chapter

In the chapter-opening Case Study (page 141), the Starnes family arrived at Old Faithful after it had erupted. They wondered how long it would be until the next eruption. Here is a scatterplot that plots the interval between consecutive eruptions of Old Faithful against the duration of the previous eruption, for the month prior to their visit.

Are there any outliers?

Oil and residuals The Trans-Alaska Oil Pipeline is a tube that is formed from 1/2-inch-thick steel and carries oil across 800miles of sensitive arctic and subarctic terrain. The pipe segments and the welds that join them were carefully examined before installation. How accurate are field measurements of the depth of small defects? The figure below compares the results of measurements on 100defects made in the field with measurements of the same defects made in the laboratory. The line y=x is drawn on the scatterplot.

(a) Describe the overall pattern you see in the scatterplot, as well as any deviations from that pattern.

(b) If field and laboratory measurements all agree, then the points should fall on the y=x line drawn on the plot, except for small variations in the measurements. Is this the case? Explain.

(c) The line drawn on the scatterplot (y=x) is not the least-squares regression line. How would the slope and y-intercept of the least-squares line compare? Justify your answer.

Dem bones Archaeopteryx is an extinct beast having feathers like a bird but teeth and a long bony tail like a reptile. Only six fossil specimens are known. Because these specimens differ greatly in size, some scientists think they are different species rather than individuals from the same species. We will examine some data. If the specimens belong to the same species and differ in size because some are younger than others, there should be a positive linear relationship between the lengths of a pair of bones from all individuals. An outlier from this relationship would suggest a different species. Here are data on the lengths in centimeters of the femur (a leg bone) and the humerus (a bone in the upper arm) for the five specimens that preserve both bones:

(a) Make a scatterplot. Do you think that all five specimens come from the same species? Explain.

(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for r. Explain how your value for rmatches your graph in (a).

Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon, left by the skeletons of single-celled creatures called diatoms, is a measure of the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look further into the past. Here is a scatterplot of data from 2300 to 12,000 years ago:

(a) Identify the unusual point in the scatterplot. Explain what鈥檚 unusual about this point.

(b) If this point was removed, describe the effect on i. the correlation.

ii. the slope and y-intercept of the least-squares line.

Should you use this line to predict the rat鈥檚 weight at age 2years? Use the equation to make the prediction and think about the reasonableness of the result. (There are454grams in a pound.)
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