 11.11.1: If 0 and 1 are the leastsquares estimates for the intercept and sl...
 11.11.2: Applet Exercise How can you improve your understanding of what the ...
 11.11.3: Fit a straight line to the five data points in the accompanying tab...
 11.11.4: Auditors are often required to compare the audited (or current) val...
 11.11.5: What did housing prices look like in the good old days? The median ...
 11.11.6: Applet Exercise Refer to Exercises 11.2 and 11.5. The data from Exe...
 11.11.7: Applet Exercise Move down to the portion of the applet labeled Curv...
 11.11.8: Laboratory experiments designed to measure LC50 (lethal concentrati...
 11.11.9: Information about eight fourcylinder automobiles judged to be amon...
 11.11.11: Some data obtained by C. E. Marcellari2 on the height x and diamete...
 11.11.12: Processors usually preserve cucumbers by fermenting them in a lows...
 11.11.14: J. H. Matis and T. E. Wehrly5 report the following table of data on...
 11.11.15: a Derive the following identity: SSE = n i=1 (yi yi) 2 = n i=1 (yi ...
 11.11.16: An experiment was conducted to observe the effect of an increase in...
 11.11.17: a Calculate SSE and S2 for Exercise 11.5. b It is sometimes conveni...
 11.11.18: a Calculate SSE and S2 for Exercise 11.8. b Refer to Exercise 11.8....
 11.11.19: A study was conducted to determine the effects of sleep deprivation...
 11.11.21: Under the assumptions of Exercise 11.20, find Cov(0, 1). Use this a...
 11.11.22: Under the assumptions of Exercise 11.20, find the MLE of 2.
 11.11.23: Refer to Exercise 11.3. a Do the data present sufficient evidence t...
 11.11.24: Refer to Exercise 11.13. Do the data present sufficient evidence to...
 11.11.25: Do the data in Exercise 11.19 present sufficient evidence to indica...
 11.11.26: Most sophomore physics students are required to conduct an experime...
 11.11.27: Use the properties of the leastsquares estimators given in Section...
 11.11.28: Suppose that Y1, Y2,..., Yn are independent, normally distributed r...
 11.11.29: Let Y1, Y2,..., Yn be as given in Exercise 11.28. Suppose that we h...
 11.11.31: Using a chemical procedure called differential pulse polarography, ...
 11.11.32: Refer to Exercises 11.5 and 11.17. a Is there sufficient evidence t...
 11.11.33: Refer to Exercise 11.8 and 11.18. Is there evidence of a linear rel...
 11.11.34: Refer to Exercise 11.33. Is there evidence of a linear relationship...
 11.11.35: For the simple linear regression model Y = 0 + 1x + with E() = 0 an...
 11.11.36: Refer to Exercise 11.13 and 11.24. Find the 90% confidence interval...
 11.11.37: Using the model fit to the data of Exercise 11.8, construct a 95% c...
 11.11.38: Refer to Exercise 11.3. Find a 90% confidence interval for E(Y ) wh...
 11.11.39: Refer to Exercise 11.16. Find a 95% confidence interval for the mea...
 11.11.41: Refer to Exercise 11.4. Suppose that the sample given there came fr...
 11.11.42: Suppose that the model Y = 0 + 1x + is fit to the n data points (y1...
 11.11.43: Refer to Exercises 11.5 and 11.17. Use the data and model given the...
 11.11.44: Refer to Exercise 11.43. Find a 95% prediction interval for the med...
 11.11.45: Refer to Exercises 11.8 and 11.18. Find a 95% prediction interval f...
 11.11.46: Refer to Exercise 11.16. Find a 95% prediction interval for the pot...
 11.11.47: Refer to Exercise 11.14. Find a 95% prediction interval for the pro...
 11.11.48: The accompanying table gives the peak power load for a power plant ...
 11.11.49: Applet Exercise Refer to Example 11.1 and Exercise 11.2. Access the...
 11.11.51: In Exercise 11.8 both the flowthrough and static LC50 values could...
 11.11.52: Is the plant density of a species related to the altitude at which ...
 11.11.53: The correlation coefficient for the heights and weights of ten offe...
 11.11.54: Suppose that we seek an intuitive estimator for = Cov(X, Y ) X Y . ...
 11.11.55: Consider the simple linear regression model based on normal theory....
 11.11.56: Refer to Exercise 11.55. Isr = .8 big enough to claim > 0 at the = ...
 11.11.57: Refer to Exercises 11.55 and 11.56. a What term in the T statistic ...
 11.11.58: Refer to Exercise 11.55. If n = 4, what is the smallest value ofr t...
 11.11.59: Refer to Exercises 11.55 and 11.58. If n = 20, what is the largest ...
 11.11.61: Refer to Example 11.10. Find a 90% prediction interval for the stre...
 11.11.62: Refer to Example 11.11. Calculate the correlation coefficientr betw...
 11.11.63: It is well known that large bodies of water have a mitigating effec...
 11.11.64: Refer to Exercise 11.14. One model proposed for these data on the p...
 11.11.65: In the biological and physical sciences, a common model for proport...
 11.11.66: Refer to Exercise 11.3. Fit the model suggested there by use of mat...
 11.11.67: Use the matrix approach to fit a straight line to the data in the a...
 11.11.68: Fit the quadratic model Y = 0 +1x +2x 2 + to the data points in the...
 11.11.69: The manufacturer of Lexus automobiles has steadily increased sales ...
 11.11.71: Consider the general linear model Y = 0 + 1x1 + 2x2 ++ k xk + , whe...
 11.11.72: Refer to Exercise 11.69. a Is there evidence of a quadratic effect ...
 11.11.73: The experimenter who collected the data in Exercise 11.68 claims th...
 11.11.74: An experiment was conducted to investigate the effect of four facto...
 11.11.75: Refer to Exercise 11.74. Find a 90% confidence interval for the exp...
 11.11.76: The results that follow were obtained from an analysis of data obta...
 11.11.77: Refer to Exercise 11.76. Give a 95% prediction interval for the per...
 11.11.78: Refer to Exercise 11.69. Find a 98% prediction interval for Lexus s...
 11.11.79: Refer to Exercises 11.74 and 11.75. Find a 90% prediction interval ...
 11.11.81: In Exercise 11.80, you used an F test to test the same hypothesis t...
 11.11.82: Refer to Exercise 11.76 where we obtained the following information...
 11.11.83: Refer to Exercises 11.76 and 11.82. Does including the variables ph...
 11.11.84: We have fit a model with k independent variables, and wish to test ...
 11.11.85: A real estate agents computer data listed the selling price Y (in t...
 11.11.86: Refer to Exercise 11.85. A realtor suspects that square footage x1 ...
 11.11.87: Does a large value of R2 always imply that at least one of the inde...
 11.11.88: Does a large value of R2 always imply that at least one of the inde...
 11.11.89: Refer to the three models given in Exercise 11.88. Let R2 I , R2 II...
 11.11.91: Refer to Exercise 11.74. Test the hypothesis at the 5% level of sig...
 11.11.92: Utility companies, which must plan the operation and expansion of e...
 11.11.93: Refer to Example 11.19. Using the reduced model, construct a 95% co...
 11.11.94: Refer to Example 11.19. Construct individual tests of the three hyp...
 11.11.95: At temperatures approaching absolute zero (273C), helium exhibits t...
 11.11.96: A study was conducted to determine whether a linear relationship ex...
 11.11.97: A response Y is a function of three independent variables x1, x2, a...
 11.11.98: If values of independent variables are equally spaced, what is the ...
 11.11.99: Suppose that you wish to fit a straight line to a set of n data poi...
 11.11.101: The data in the accompanying table come from the comparison of the ...
 11.11.102: The following model was proposed for testing whether there was evid...
 11.11.103: Show that the leastsquares prediction equation y = 0 + 1x1 ++ k xk...
 11.11.104: An experiment was conducted to determine the effect of pressure and...
 11.11.105: Let (X, Y ) have a bivariate normal distribution. A test of H0: = 0...
 11.11.106: Labor and material costs are two basic components in the cost of co...
 11.11.107: The data in the following table give the miles per gallon obtained ...
 11.11.108: Applet Exercise Access the applet Removing Points from Regression. ...
Solutions for Chapter 11: Linear Models and Estimation by Least Squares
Full solutions for Mathematical Statistics with Applications  7th Edition
ISBN: 9780495110811
Solutions for Chapter 11: Linear Models and Estimation by Least Squares
Get Full SolutionsSince 97 problems in chapter 11: Linear Models and Estimation by Least Squares have been answered, more than 140924 students have viewed full stepbystep solutions from this chapter. Chapter 11: Linear Models and Estimation by Least Squares includes 97 full stepbystep solutions. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7. This expansive textbook survival guide covers the following chapters and their solutions.

Additivity property of x 2
If two independent random variables X1 and X2 are distributed as chisquare with v1 and v2 degrees of freedom, respectively, Y = + X X 1 2 is a chisquare random variable with u = + v v 1 2 degrees of freedom. This generalizes to any number of independent chisquare random variables.

Axioms of probability
A set of rules that probabilities deined on a sample space must follow. See Probability

Categorical data
Data consisting of counts or observations that can be classiied into categories. The categories may be descriptive.

Chisquare test
Any test of signiicance based on the chisquare distribution. The most common chisquare tests are (1) testing hypotheses about the variance or standard deviation of a normal distribution and (2) testing goodness of it of a theoretical distribution to sample data

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Conditional probability mass function
The probability mass function of the conditional probability distribution of a discrete random variable.

Control chart
A graphical display used to monitor a process. It usually consists of a horizontal center line corresponding to the incontrol value of the parameter that is being monitored and lower and upper control limits. The control limits are determined by statistical criteria and are not arbitrary, nor are they related to speciication limits. If sample points fall within the control limits, the process is said to be incontrol, or free from assignable causes. Points beyond the control limits indicate an outofcontrol process; that is, assignable causes are likely present. This signals the need to ind and remove the assignable causes.

Control limits
See Control chart.

Convolution
A method to derive the probability density function of the sum of two independent random variables from an integral (or sum) of probability density (or mass) functions.

Critical region
In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis.

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Erlang random variable
A continuous random variable that is the sum of a ixed number of independent, exponential random variables.

Extra sum of squares method
A method used in regression analysis to conduct a hypothesis test for the additional contribution of one or more variables to a model.

False alarm
A signal from a control chart when no assignable causes are present

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Forward selection
A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signiicantly to the model can be found.

Fractional factorial experiment
A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.

Frequency distribution
An arrangement of the frequencies of observations in a sample or population according to the values that the observations take on