Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Question
Chapter 14.1, Problem 1E
a.
To determine
Explain the difference between a deterministic and a probabilistic model.
b.
To determine
Explain an example for a deterministic way.
c.
To determine
Explain an example for a probabilistic way.
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Exercise 4.
Mary is investigating the determinants of house prices in 90 cities. She gathers information on house
value in log (Inhseval), the size of the house (sizehse), and income per capita in log (Inincome). She
also gathers information on the property tax rate, specifically if cities have the low property tax rate
(less than 2.5%), or the high property tax rate (2.5% or more). She runs the following regression:
Ln(hseval;)= a + B₁(sizehse;) + B2 (income)+ &;
And then she separates the regression by low and high property tax rate.
The results of her regression analysis are given in the tables below.
Regression results: Dependent variable is Ln(hseval;)
Source
Model
Residual
Total
1nhseval.
sizehse
Inincome
cons
Source
Model
Residual
-> lowtax High tax rate
Total
1nhseval
sizehse
inincome
_cons
Source
Model
Residual
Total
SS
1nhseval
1.56064571
2.98039214
4.54103785
sizehse
inincome
_cons
SS
-> lowtax Low tax rate
Coef. Std. Err.
.4007332 .088795
.6444489 .2287038
-4.40504 1.722207…
The manager of Gilley’s Ice Cream Parlor needs an accurate forecast of the demand for ice cream. The store orders ice cream from a distributor a week ahead; if the store orders too little, it loses business, and if it orders too much, the extra must be thrown away. The manager believes that a major determinant of ice cream sales is temperature (i.e., the hotter the weather, the more ice cream people buy). Using an almanac, the manager has determined the average daytime temperature for 10 weeks, selected at random, and from store records he has determined the ice cream consumption for the same 10 weeks. These data are summarized as follows: a. Develop a linear regression model for these data and forecast the ice cream consumption if the average weekly daytime temperature is expected to be 85 degrees. b. Determine the strength of the linear relationship between temperature and ice cream consumption by using correlation.
The equation for a straight line (deterministic model) is y=β0+β1x.
If the line passes through the point (−10,10), then x = −10, y = 10 must satisfy the equation; that is, 10=β0+β1(−10).
Similarly, if the line passes through the point (3,12), then x = 3, y = 12 must satisfy the equation; that is, 12=β0+β1(3).
Use these two equations to solve for β0 and β1; then find the equation of the line that passes through the points (−10,10) and (3,12).
A. Find β0 and β1.
β1 =
β0 =
(Simplify your answers. Type integers or simplified fractions.)
Chapter 14 Solutions
Introduction to Statistics and Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 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. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 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. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
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