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Chapter 12: Q. 9 (page 797)

Which of the following would provide evidence that a power law model of the form y=axbwhere b鈮�0andb鈮�1, describes the relationship between a response variable yand an explanatory variable x.

(a) A scatterplot of yversus xlooks approximately linear.

(b) A scatterplot of ln yversus xlooks approximately linear.

(c) A scatterplot of yversus ln xlooks approximately linear.

(d) A scatterplot of ln yversus ln xlooks approximately linear.

(e) None of these.

Short Answer

Expert verified

A scatterplot of in lnyversus in lnxlooks approximately linear. Therefore the correct option is d.

Step by step solution

01

Given Information

A power law model of the form y=axbwhere b鈮�0and b鈮�1describes the relationship between a response variableyand an explanatory variablex.

02

Explanation

The scatterplot of a power model has become linear if we convert both variables to its logarithms. In the options (a) and (b) both variables are without logarithms and in the option (c) only one variable in logarithms.

Thus, the correct option is (d).

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Most popular questions from this chapter

In the casting of metal parts, molten metal flows through a 鈥済ate鈥� into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminium pistons examined a random sample of 12pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process. A scatterplot of the data is shown below

A least-squares regression analysis was performed on the data. Some computer output and a residual plot are shown below. A Normal probability plot of the residuals (not shown) is roughly linear.

Do these data provide convincing evidence of a straight-line relationship between thickness and gate velocity in the population of pistons formed from this alloy of metal? Carry out an appropriate significance test at the 伪=0.05level.

In the casting of metal parts, molten metal flows through a 鈥済ate鈥� into a die that shapes the part. The gate velocity (the speed at which metal is forced through the gate) plays a critical role in die casting. A firm that casts cylindrical aluminum pistons examined a random sample of 12 pistons formed from the same alloy of metal. What is the relationship between the cylinder wall thickness (inches) and the gate velocity (feet per second) chosen by the skilled workers who do the casting? If there is a clear pattern, it can be used to direct new workers or to automate the process.

Construct and interpret a 95%confidence interval for the slope of the population regression line. Explain how this interval is consistent with the results of Exercise R12.2.

A random sample of 900students at a very large university was asked which social-networking site they used most often during a typical week. Their responses are shown in the table below.

Assuming that gender and preferred networking site are independent, which of the following is the expected count for female and LinkedIn?

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Growth hormones are often used to increase the weight gain of chickens. In an experiment using 15chickens, five different doses of growth hormone (0, 0.2, 0.4, 0.8, and 1.0milligrams) were injected into chickens (3chickens were randomly assigned to each dose), and the subsequent weight gain (in ounces) was recorded. A researcher plots the data and finds that a linear relationship appears to hold. Computer output from a least-squares regression analysis for these data is shown below.

role="math" localid="1652870715985" PredictorCoefSE CoefTPConstant4.54590.61667.37<0.0001Dose4.83231.01644.750.0004S=3.135R-Sq=38.4%R-Sq(adj)=37.7%

(a) What is the equation of the least-squares regression line for these data? Define any variables you use.

(b) Interpret each of the following in context:

(i) The slope

(ii) The yintercept

(iii) s

(iv) The standard error of the slope

(v) r2

(c) Assume that the conditions for performing inference about the slope B of the true regression line are met. Do the data provide convincing evidence of a linear relationship between dose and weight gain? Carry out a significance test at the A 伪=0.05level.

(d) Construct and interpret a 95%confidence interval for the slope parameter.

Inference about the slope 尾of a least-squares regression line is based on which of the following distributions?

(a) The t distribution with n-1degrees of freedom

(b) The standard Normal distribution

(c) The chi-square distribution with n-1degrees of freedom

(d) The t distribution with n-2degrees of freedom

(e) The Normal distribution with mean 渭and standard deviation蟽

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