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Chapter 12: Q.1.2 (page 777)

Give the equation of the least-squares regression line. Define any variables you use.

Short Answer

Expert verified

The equation of the least-squares regression line is y^=-1.19311+0.0287280x.

Step by step solution

01

Given Information

02

Explanation

In the question that variable xbe the number of the years since 1700and the variable y be the U.S. population in the years 1790to 1880. Thus, the general equation will be as:

y^=a+bx

And the slope and the constant of the regression line is give in the previous question as:

a=-1.19311

b=0.0287280

Thus, the regression line is as:

y^=a+bx

鈬�y^=-1.19311+0.0287280x

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Most popular questions from this chapter

6. Beer and BAC Refer to Exercise 4. Computer output from the least-squares regression analysis on the beer and blood alcohol data is shown below.


The model for regression inference has three parameters:伪,尾and蟽Explain what each parameter represents in context. Then provide an estimate for each.

Determining tree biomass It is easy to measure the 鈥渄iameter at breast height鈥� of a tree. It鈥檚 hard to measure the total 鈥渁boveground biomass鈥� of a tree, because to do this you must cut and weigh the tree. The biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. Combining data on 378trees in tropical rain forests gives this relationship between biomass y measured in kilograms and diameter x measured in centimeters:

lny^=-2.00+2.42lnx

A large machine is filled with thousands of small

pieces of candy, 40%of which are orange. When money

is deposited, the machine dispenses 60randomly selected

pieces of candy. The machine will be recalibrated if a

group of 60candies contains fewer than18 that are

orange. What is the approximate probability that this will

happen?

a)Pz<0.3-0.4(0.4)(0.6)60

b)Pz<0.4-0.3(0.3)(0.7)60

role="math" localid="1650519113387" c)Pz<0.3-0.4(0.4)(0.6)60

role="math" localid="1650519757907" d)Pz<0.3-0.4(0.4)(0.6)60

e)Pz<0.4-0.3(0.3)(0.7)60

Insurance adjusters are always vigilant about being overcharged for accident repairs. The adjusters suspect that Repair Shop 1quotes higher estimates than Repair Shop 2. To check their suspicion,

the adjusters randomly select 12cars that were recently involved in an accident and then take each of the cars to both repair shops to obtain separate estimates of the cost to 铿亁 the vehicle. The

estimates are given below in hundreds of dollars.


Assuming that the conditions for inference are reasonably met, which of the following signi铿乧ance tests could legitimately be used to determine whether the adjusters鈥� suspicion is correct?

I. A paired ttest

II. A two-sample ttest

III. A t test to see if the slope of the population regression line is 0.

(a) I only

(b) II only

(c) I and III

(d) II and III

(e) I, II, and III

Which of the following statements about the t distribution with degrees of freedom df is (are) true?

I. It is symmetric.

II. It has more variability than the t distribution with df+1degrees of freedom.

III. As df increases, the t distribution approaches the standard Normal distribution.

(a) I only (c) III only (e) I, II, and III

(b) II only (d) I and II
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