In each of the following settings, give the values of a and b for the linear transformation xnew = a + bx that expresses the change in units of measurement.

You want to restate water temperature x in a swimming pool, measured in degrees Fahrenheit, as xnew, the number of degrees the pool water temperature is below "normal" body temperature of 98.6 degrees.

a = 98.6
b = ?

If the water temperature x in several swimming pools has standard deviation s = 3.1 degrees Fahrenheit, what is the standard deviation of xnew in these swimming pools?
______degrees Fahrenheit

does this make sense to anyone? becuz i am lost!

2/8/2007 5:49:28 PM

I might be wrong but i think that

xnew = 98.6 - (1)x where a = 98.6 and b = -1

Then if s = 3.1, s^2 is 9.61. When you do a linear transformation (a) has no affect on the variance or standard deviation but you square b times the original standard deviation. So, in this case it would be snew^2 = (-1)^2*9.61 so snew = s = 3.1. Not sure if that's right, but I gave it a stab.

2/8/2007 6:47:07 PM

Yep, philly's right

2/8/2007 6:49:42 PM

ahh thanks

2/8/2007 7:10:31 PM

without even thinking about the math, it seems obvious to me the answer is s=3.1

because why would the std. dev. be any different if the sample values were referenced to zero, or referenced to any arbitrary point.

deviation is deviation no matter which direction you look from.

2/9/2007 2:39:29 AM

can anyone figure this problem out?...

Question 1.

Financial institutions use logistic regression to produce an estimate of the probability p that an applicant will repay his or her loan. If the estimated probability is too low, the applicant will not be granted the loan. Financial institutions use the data from thousands of previous applications and whether the loans were fully repaid to determine a logistic regression equation. The logistic regression equation converts the information contained in a loan application to an estimate of the probability p that the applicant will repay the loan.

To evaluate new loan applications, the Dewey, Cheatem, and Howe Loan Company uses the following logistic regression equation:

ln(y^^\^) = a + b1x1 + b2x2 + b3x3 + b4x4

where

y^^\^ = Estimated odds ratio of repaying the loan

x1 = Age

x2 = Income ($1,000s)

x3 = Time at current job (years)

x4 = Time at current address (years)

The coefficients in the logistic regression equation are:

a = .1524

b1 = .0281

b2 = .0223

b3 = .0152

b4 = .0114

Dewey, Cheatem, and Howe Loan Company has received loan applications from 3 people. Data from their loan applications is shown in the following table. Dewey, Cheatem, and Howe would like to estimate the probability p that each applicant will repay the loan.

Applicant Age Income ($1,000s) Years at Current Job Years at Current Address
1 27 55 6 5
2 48 78 3 12
3 37 39 12 10

Question 1a. Find the odds ratio for each applicant.
(Use 4 decimal places)

odds ratio for applicant 1

odds ratio for applicant 2

odds ratio for applicant 3

Question 1b. For each applicant, find the probability that the applicant will repay the loan.
(Use 4 decimal places)

probability applicant 1 will repay loan

probability applicant 2 will repay loan

probability applicant 3 will repay loan

Question 2.

Sunday, February 1, 2004, a day that will live in infamy: kicker Adam Vinatieri of the evil New England Patriots kicked a game-winning 41-yard field goal with 9 seconds remaining in Super Bowl XXXVIII to beat the beloved and underdog Carolina Panthers 32-29. Prior to the kick, what was the probability Vinatieri's kick would be successful? More generally, prior to a field goal attempt by a National Football League (NFL) placekicker from distance x, what is the estimated probability of success?

For those of you not familiar with American football (as opposed to futbol played with a round ball), the objective of a field goal attempt is to kick the football, while it is held in place on the ground by a teammate, over the crossbar and between the uprights of the goalpost. A successful field goal is worth 3 points to the kicking team.

In this problem you will estimate the probability p of a successful field goal attempt, as a function of the distance x of the attempt, using logistic regression. The data used consists of the results of 662 recent field goal attempts in the NFL. For each attempt the distance x (in yards) and outcome (successful = 1, unsuccessful = 0) was recorded. The resulting logistic regression equation is as follows:

ln(y^^\^) = a + bx

where

y^^\^ = Estimate of odds ratio of successful field goal attempt

x = distance (in yards) of field goal attempt

The coefficients of the logistic regression equation are

a = 4.5156

b = -.0859

Note:Right click here and choose "Open link in new window" to see a graph of the field goal success probability p vs distance x.

Question 2a. From a distance of 25 yards, what is the estimated probability p of a successful field goal?
(use 4 decimal places)

Question 2b. From a distance of 30 yards, what is the estimated probability p of a successful field goal?
(use 4 decimal places)

Question 2c. Prior to his infamous kick, what was the estimated success probability p of Adam Vinatieri's 41-yard attempt mentioned at the beginning of the problem?
(use 4 decimal places)

Question 2d. If the New England Patriots had been penalized 5 yards, thus forcing Vinatieri to kick from 46 yards, what is the estimated success probability?
(use 4 decimal places)

3/2/2007 10:47:23 PM

my god...

unbelievable.

that 1st q at the top is basically like converting from Fahrenheit to Celsius.

and that is taught in what, grade 9?

jesus.

3/2/2007 10:54:44 PM

im in yo class, if u need help with the webassigns pm me

3/2/2007 11:08:31 PM

the answer is 42.

3/5/2007 1:08:13 AM

If you dont know these questions, then the Game's Over For You

3/5/2007 1:58:27 AM

Yeah, seriously. This is just algebra. The problems tells you all the formulas and values. You've got to put more effort into your studies if you can't understand this.

3/5/2007 10:03:13 AM