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Chapter 4: Q. 4.68 (page 175)

Age and Price of Orions. In Table 4.2, we provided data on age and price for a sample of 11Orions between 2and 7years old. On the Weiss Stats site, we have given the ages and prices for a sample of 31Orions between 1and 11years old.

a. Obtain a scatterplot for the data.

b. Is it reasonable to find a regression line for the data? Explain your answer.

Short Answer

Expert verified

a. The scatterplot for the given data is,

b. Yes, it is reasonable to find a regression line for the data.

Step by step solution

01

Part (a) Step 1: Given Information

Table 4.2measures the age and price of 11onions. The age is indicated in years and the price is shown in hundreds of dollars.

02

Part (a) Step 2: Explanation 

According to the graph, the age is on the horizontal axis and the price is on the vertical axis.

03

Part (b) Step 1: Given Information

The purpose of this explanation is to demonstrate the reasonableness of the regression line's finding.

04

Part (b) Step 2: Explanation 

Based on the above plot, it's evident that there is no strong curvature and the pattern of the scatter plot is fairly linear.

In other words, onions' price increases linearly with their age.

Therefore, it is reasonable to assume that there is a linear relationship between the two.

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Most popular questions from this chapter

Corvette Prices. The Kelley Blue Book provides information on wholesale and retail prices of cars. Following are age and price data for 10 randomly selected Corvettes between 1 and 6 years old.

Here, xdenotes age, in years, and ydenotes price, in hundreds of dollars. For part (g). predict the prices of a 2 -year-old Corvette and a 3-year-old Corvette.

  1. find the regression equation for the data points.
  2. graph the regression equation and the data points.
  3. describe the apparent relationship between the two variables under consideration.
  4. interpret the slope of the regression line.
  5. identify the predictor and response variables.
  6. identify outliers and potential influential observations.
  7. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.

Road Grade. The grade of a road is defined as the distance it rises (or falls) to the distance it runs horizontally, usually expressed as a percentage. Consider a road with a positive grade, g. Suppose that you begin driving on that road at an altitude a0

a. Find the linear equation that expresses the altitude, a, when you have driven a distance, d,along the road. (Hint: Draw a graph and apply the Pythagorean Theorem

b. Identify and interpret the y-intercept and slope of the linear equation in part (a).

c. Apply your results in parts (a) and (b) to a road with a 5%grade and an initial altitude of 1mile. Express your answer for the slope to four decimal places.

d. For the road in part (c). what altitude will you reach after driving 10milesalong the road?

e. For the road in part (c), how far along the road must you drive to reach an altitude of 3miles?

Estriol Level and Birth Weight. J. Greene and J. Touchstone conducted a study on the relationship between the estriol levels of pregnant women and the birth weights of their children. Their findings. "Urinary Tract Estriol: An Index of Placental Function," were published in the American lournal of obstetrics and Gynecology (Vol. 85(1). pp. 1-9). The data from the study are provided on the WeissStats site, where estriol levels are in mg/24hrbirth weights are in hectograms.

a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b) (d).

b. Obtain the coefficient of determination.

c. Determine the percentage of variation in the observed values of the response variable explained by the regression. and interpret your answer.

d. State how useful the regression equation appears to be for making predictions.

Fill in the blanks.

a. In the context of regression, an_______ is a data point that lies far from the regression line, relative to the other data points.

b. In regression analysis, an_______ is a data point where removal causes the regression equation to change considerably:

(a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables for x,y,e,e2,y^

(c) Determine which line fits the data points better according to the least-square criterion.
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