Prove the following statement. Allow the data x1,..xn to have s ample mean of x and sample variance of s. If the data is transformed by the equation yi = a + b*xi, then the mean of the %3D transformed data will be a + bx and the sample variance will be b2* s,?

Prove the following statement. Allow the data x1,..xn to have s ample mean of x and sample variance of s. If the data is transformed by the equation yi = a + bxi, then the mean of the %3D transformed data will be a + bx and the sample variance will be b2 s,?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter1: Functions

Section1.2: The Least Square Line

Problem 8E

See similar textbooks

Related questions

Q: Which of the following equations is the formula used to estimate the numerical characteristics of…

Q: 5. When Y is regressed on X, B1 < 0, sx±0, sy± 0, and sý + sỷ. In this example, the sum of the…

A: Regression predicts the value of dependent variable by using one or more independent variables.

Q: If X is normally distributed with a mean of 6 and a variance of 25, P(|X-6|<5) P(|X-6|<10)…

A: As per guideline expert have to answer first three subparts only dear student please upload other…

Q: QUESTION 18 Y 6. 6. 10 8. 10 10 12 10 12 10 What is the variance accounted for in Y by X? .50

A: Answer- GIven X Y 6 6 10 8 10 10 12 10 12 6 10 8

Q: QUESTION 14 Given the intercept on y axis to be 31 and Sxx33445 and Sxy 2004 for given y = 80, the…

Q: We are interested in determining whether or not the variances of the sales at two small grocer of 21…

A: Given: Store A: n1=21, S12=800 Store B: n2=16, S22=400

Q: 1. Suppose X1,X2,...,Xn is a random sample of size n > 5 that comes from a distribution with E[X] =…

A: X1 , X2, .... , Xn are samples from a distribution with E(X) = µ and Var(X) = σ2 There are two…

Q: Given that SST = 270, R² = 0.75 and n = 40, then the model error variance is O a. 1.677 O b. 2.677…

Q: For an AR(1) model with Y = 7.5, ø = -0.6, µ = 5, and o? = 1, %3| %3D (a) Find Ý(1), Ý;(2), and…

Q: If E(x; – X)² fi = 600 and E f; = 30 , The variance value is equal to %3D

A: The variance is calculated by Variance= (1/N) sigma fi(xi - X)^2

Q: QUESTIONS 6-11 ARE RELATED TO THE FOLLOWING Now consider the textbook expense of all IUPUI students.…

Q: If X is an unknown with the only possible values 11,12,13,14, or 15, and all are equally likely as…

A: Given that, X is an unknown with all possible values 11, 12, 13, 14 or 15. These given values of X…

Q: If E(X) = 6 and E[(X) (X-1) ] = 51, find the second moment= 1 and the variance of X= 2

A: Given Data: E(X)=6 E[(X) (X-1)]=51

Q: If X1, X2, and X3 are independent and have the means4, 9, and 3 and the variances 3, 7, and 5, find…

A: The variables X1, X2, and X3 are independent.

Q: The following estimator for the population variance 1 (T; – a)? n i=1 is

Q: Suppose that E (0₂) = E(0₂) = = 0, var(0₂) = ₁, var(8₂) = ₂. Consider the following estimator ₂ = a₁…

A: Estimator An estimator is a rule for calculating an estimate of a given quantity supported by…

Q: Ex:- let S2 be the variance of ar.s of size six from N(u,12) find Pr(2.30 < S² < 22.2)

A: Given: Sample size n=6 σ2=12 We have to find P2.30<S2<22.2 First we must change the…

Q: For an AR(1) model with Y = 7.5, o = -0.6, µ= 5, and o? = 1, %3D %3D (a) Find Y(1), Ý(2), and Ý:(6).…

Q: Given that SST= 270, R2 = 0.75 and n = 40, then the model error variance is O a. 1.677 O b. 2.677 O…

Q: X and Y are independent. If we are given P(X = 0) = P(X =1) = P(X =2) = }, P(Y = 1) = 3. P(Y = 2) =…

A: The question is simple and formula based, we need to know the mathematical formulas which are used…

Q: One sample has SS = 48 and a second sample has SS = 42. Now assume that n = 4 for the first sample…

A: We have given that, For first sample :- SS1 = 48, n1 = 4 and SS2 = 42, n2 = 8 Then, We will find…

Q: The following 94% C.I. for µ was obtained from a sample of 27 observations (the population variance…

A: Given confidence interval of 94% for mean = (-221.9745, 60.1727)sample size = 27Population variance…

Q: Given that SST= 270, R2 = 0.75 and n = 40, then the model error variance is %3D Oa. 2.776 O b. 1.677…

A: Given, SST=270R2=0.75n=40 Error variance formula: S2=SSEn-2

Q: In a population with o= 4, a score of X= 48 corresponds to z = 1.50. The mean for this population is…

Q: 1.For a symmetric data set with a mean of 11 and a variance of 25, approximately 68% of the values…

A: Solution: Given information: μ= 11 Population mean σ2= 25 Population variance σ= σ2σ=25σ= 5…

Q: Suppose X has the following PMF. Show all your work. -2, with probability 1/4, 0, with probability…

A: From the given information, The PMF can be shown in the table form below: X P(X=x) -2 1/4 0…

Q: 2. The mean of X = 10 and the standard deviation of X = 2. The variable X is linearly transformed…

Q: Find the variance. Si f 2 4 4 7 6 3 O A) 4,54 B) 1,46 C) 2,13 O D) 27,72 E) 3,12

A: Measures of Dispersion: The word dispersion is used to denote the degree of heterogeneity in the…

Q: If X Gamma(4,6) the the variance of X is 4 24 144

Q: Consider the following data points, where the first coordinate corresponds to x and the second…

A: Consider the missing value as "c". Now, the given data will be, x y 0 1 1 1 2 0 3 c…

Q: If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of…

Q: Let X1, X2,...,X3 denote a random sample from a population having mean u and variance o?. Which of…

Q: Suppose these measurements as random variables, where X has the mean of 1 and standard deviation of…

Q: a. Suppose X and Y are independent, X has mean 5 and variance 7, Y has mean -3 and variance 8.…

A: Here AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION ONLY PLZ REPOST FOR REMAINING PARTS

Q: In many problems we interested in estimation of the population mean. Let X1,., X10 be a random…

Q: Suppose X and Y are independent, X has mean 5 and variance 9, Y has mean -3 and variance 6. Compute…

Q: 8- Find the mean and variance of X? X 0 1 2 4 f(x) 1/9 2/9 3/9 2/9 1/9 a) 3, 2/3 1903 b) O 2, 4/3 c)…

A: From the data given x f(x) x f(x) x2 f(x) 0 1/9 0 0 1 2/9 2/9 2/9 2 3/9 6/9 12/9 3 2/9…

Q: iance σ2 = 0.

A: According to the given sum, weights of college mathematics textbooks in the United States are…

Q: We have the following information about the random variables X and Y: 0.5, дY – 1,o = 1, o = 2.25.…

Q: Two weights, each labeled as weighing 100 g, are each weighed several times on the same scale. The…

A: Note: in this scenario, MINITAB software is used to obtain two-sample t test. The data represents…

Q: use the following information to answer question . n = 6 , σ x = 16, σ x2 = 72. the variance s2 is

A: It is given that, n = 6, Σx = 16, Σx2 = 72.

Q: 4. From a data ,the following measures are obtained SSXY = 345, SSy = 363 and SSyy = 643. The…

A: In simple linear regression, there will be only one independent variable and one dependent variable.…

Q: The following table consists of one student athlete's time, x, (in minutes) to swim 2,500 yards and…

A: Given - x is athlete's time (in minutes) to swim 2,500 yards y is heart rate (beats per minute)

Q: Let X have a mean of 13 and a variance of 1.1. Let Y have a mean of 9.1 and a variance of 0.75. The…

Q: If all rhe scores in a set of test scores were the same , the variance would be equal to : a. 0 b.…

A: Solution :The Formula for variance is :Variance Σxi-x2n

Q: Consider the following hypothesis statement using a = 0.05 and data from two independent samples.…

Q: Consider R.V. Y Unif (0, 1) What is the variance of U -4 In(Y)? %D

A: From the given information, Y~Unif0,1. f(y)=11-0 =1, 0<y<1

Question

Prove the statement

Prove the following statement. Allow the data x1,...xn to have s ample mean of x and sample
variance of s,. If the data is transformed by the equation yi = a + b*xi, then the mean of the
transformed data will be a + bx and the sample variance will be b2* s,

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Truth Tables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.