The ability to estimate the volume of a tree based on a simple measurement, such as the tree’s diameter, is important to the lumber industry, ecologis

OlmekinjP 2020-11-12 Answered
The ability to estimate the volume of a tree based on a simple measurement, such as the tree’s diameter, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines were reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Fatema Sutton
Answered 2020-11-13 Author has 88 answers

Given: n= Sample size =70 a) Diameter is on the horizontal axis and Volume is on the vertical axis. image b) It is reasonable to find a regression lien for the data if there is no strong curvature present in the scatterplot. We note that there is no strong curvature in the scatterplot of part (a) and thus it is reasonable to find a regression line for the data. c) Let us first determine the necessary sums:  xi=782.9
 xi2=9934.65
 yi=2442.7
 xiyi=35376.74 Next, we can determine Sxx and Sxy
Sxx=  xi2  ( xi)2n=9934.65  782.9270=1178.4727
Sxy=  xiyi  ( xi)( yi)n=35376.74  782.9  2442.770=8056.8853 The estimate b of the slope β is the ratio of Sxy and Sxx:
b= SxySxx= 8056.88531178.4727=6.8367 The mean is the sum of all values divided by the number of values: x=  xin= 782.970=11.1843
y=  yin= 2442.770=34.8957 The estimate a of the intercept α is the average of y decreased by the product of the estimate of the slope and the average of x. a= y  b x=34,8957  6,8367  11,1843= 41,5681 General least-squares equation: y^= α + β x Replace α by a= 41.5681 and β by b=6.8367 in the general least-squares equation: y=a + bx= 41.5681 + 6.8367x d) There appear to be one outliers, because the point in the top right corner of the scatterplot list more to the right than all other points in the scatterplot. There appear to be no influential observations beside the outlier, because all data values lie near the regression line except fro the outlier. e) Let us first determine the necessary sums:  xi=759.5
 xi2=9387.09
 yi=2279.2
 xiyi=31550.84 Next, we can determine

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-02-22
Use the technology of your choice to do the following tasks. In the article “Statistical Fallacies in Sports” (Chance, Vol. 19, No. 4, pp. 50-56), S. Berry discussed, among other things, the relation between scores for the first and second rounds of the 2006 Masters golf tournament. You will find those scores on the WeissStats CD. For part (d), predict the secondround score of a golfer who got a 72 on the first round. a) Construct and interpret a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)–(f). c) Determine and interpret the regression equation. d) Make the indicated predictions. e) Compute and interpret the correlation coefficient. f) Identify potential outliers and influential observations.
asked 2021-01-30
Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be a great danger to natural ecosystems. In a study by R. W. Risebrough titled “Effects of Environmental Pollutants Upon Animals Other Than Man” (Proceedings of the 6th Berkeley Symposium on Mathematics and Statistics, VI, University of California Press, pp. 443-463), 60 Anacapa pelican eggs were collected and measured for their shell thickness, in millimeters (mm), and concentration of PCBs, in parts per million (ppm). a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)–(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.
asked 2021-11-16
Make a scatterplot for the data below on the number of people working on farms in various years, and draw a line of best fit. Describe the correlation as strong positive, strong negative, or little to none.
Year194019501960197019801990Number of farm workers in thousands899568584132288128182864
asked 2021-01-31
The Information Please Almanac provides data on the ages at inauguration and of death for the presidents of the United States. We give those data on the WeissStats CD for those presidents who are not still living at the time of this writing. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.
asked 2022-03-26
asked 2021-07-04

Using the daily high and low temperature readings at Chicago's O'Hare International Airport for an entire year, a meteorologist made a scatterplot relating y = high temperature to x = low temperature, both in degrees Fahrenheit.

After verifying that the conditions for the regression model were met, the meteorologist calculated the equation of the population regression line to be  [μy=16.6+1.02]with[σ=6.6+F]

If the meteorologist used a random sample of 10 days to calculate the regression line instead of using all the days in the year, would the slope of the sample regression line be exactly 1.02? Explain your answer.

asked 2021-02-24
The document Arizona Residential Property Valuation System, published by the Arizona Department of Revenue, describes how county assessors use computerized systems to value single-family residential properties for property tax purposes. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

New questions