Introduction To Statistics And Data Analysis

6th Edition

ISBN: 9781337793612

Author: PECK, Roxy.

Publisher: Cengage Learning,

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…

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Textbook Question

Chapter 14.1, Problem 10E

The relationship between yield of maize (a type of com), date of planting, and planting density was investigated in the article “Development of a Model for Use in Maize Replant Decisions” (Agronomy Journal [1980]: 459-464). Let

y = Maize yield (percent)

x₁ = Planting date (days after April 20)

x₂ = Planting density (10.000 plants/ha)

The regression model with both quadratic terms (y = α + β₁x₁ + β₂x₂ + β₃x₃ + β₄x₄ + e where x₃ = x 1 2 and x₄ = x 2 2 ) provides a good description of the relationship between y and the independent variables.

a. If α = 21.09, β₁ = 0.653, β₂ = 0.0022, β₃ = 2.0206, and β₄ = 0.4, what is the population regression function?
b. Use the regression function in Part (a) to determine the mean yield for a plot planted on May 6 with a density of 41,180 plants/ha.
c. Would the mean yield be higher for a planting date of May 6 or May 22 (for the same density)?
d. Is it appropriate to interpret β₁ = 0.653 as the average change in yield when planting date increases by one day and the values of the other three predictors are held fixed? Why or why not?

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 14.1, Problem 9E

Chapter 14.1, Problem 11E

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We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.

The relationship between yield of maize (a type of corn), date of planting, and planting density was investigated in an article. Let the variables be defined as follows. y = maize yield (percent) x1 = planting date (days after April 20) x2 = planting density (10,000 plants/ha) The following regression model with both quadratic terms where x3 = x12 and x4 = x22 provides a good description of the relationship between y and the independent variables. y = ? + ?1 x1 + ?2 x2 + ?3 x3 + ?4 x4 + e (a) If ? = 21.05, ?1 = 0.652, ?2 = 0.0025, ?3 = −0.0204, and ?4 = 0.5, what is the population regression function? y = (b) Use the regression function in part (a) to determine the mean yield (in percent) for a plot planted on May 8 with a density of 41,182 plants/ha. (Round your answer to two decimal places.) % (c) Would the mean yield be higher for a planting date of May 8 or May 22 (for the same density)? The mean yield would be higher for . (d) Is it…

An attempt was made to construct a regression model explaining student scores in intermediate economics courses (Waldauer, Duggal, and Williams 1992). The population regression model assumed thatY = total student score in intermediate economics coursesX1 = mathematics score on Scholastic Aptitude TestX2 = verbal score on Scholastic Aptitude TestX3 = grade in college algebra (A = 4, B = 3, C = 2, D = 1)X4 = grade in college principles of economics courseX5 = dummy variable taking the value 1 if the student is female and 0 if maleX6 = dummy variable taking the value 1 if the instructor is male and 0 if femaleX7 = dummy variable taking the value 1 if the student and instructor are the same gender and 0 otherwiseThis model was fitted to data on 262 students. Next we report t-ratios, so that tj is the ratio of the estimate of bj to its associated estimated standard error. These ratios are as follows:t1 = 4.69, t2 = 2.89, t3 = 0.46, t4 = 4.90,t5 = 0.13, t6 = -1.08, t7 = 0.88The objective of…

Chapter 14 Solutions

Introduction To Statistics And Data Analysis

Ch. 14.1 - Prob. 1E Ch. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - The relationship between yield of maize (a type of...

Ch. 14.1 - Prob. 11E Ch. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13E Ch. 14.1 - Prob. 14E Ch. 14.1 - Prob. 15E Ch. 14.2 - Prob. 16E Ch. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18E Ch. 14.2 - Prob. 19E Ch. 14.2 - Prob. 20E Ch. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22E Ch. 14.2 - Prob. 23E Ch. 14.2 - Prob. 24E Ch. 14.2 - Prob. 25E Ch. 14.2 - Prob. 26E Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28E Ch. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30E Ch. 14.2 - Prob. 31E Ch. 14.2 - Prob. 32E Ch. 14.2 - Prob. 33E Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36E Ch. 14.3 - Prob. 37E Ch. 14.3 - When Coastal power stations take in large amounts...Ch. 14.3 - Prob. 39E Ch. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43E Ch. 14.3 - Prob. 44E Ch. 14.3 - Prob. 45E Ch. 14.3 - Prob. 46E Ch. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48E Ch. 14.3 - Prob. 49E Ch. 14.3 - Prob. 50E Ch. 14.4 - Prob. 51E Ch. 14.4 - Prob. 52E Ch. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54E Ch. 14.4 - Prob. 55E Ch. 14.4 - Prob. 57E Ch. 14.4 - Prob. 58E Ch. 14.4 - Prob. 59E Ch. 14.4 - Prob. 60E Ch. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62E Ch. 14 - Prob. 63CR Ch. 14 - Prob. 64CR Ch. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CR Ch. 14 - Prob. 68CR Ch. 14 - Prob. 69CR Ch. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CR Ch. 14 - Prob. 72CR Ch. 14 - This exercise requires the use of a statistical...

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Solution Summary: The author calculates the population regression equation by substituting the corresponding values in the regression model.

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