Question

In: Statistics and Probability

1) Generate a data set with three variables (X, Y and Z). X and Y have...

1) Generate a data set with three variables (X, Y and Z). X and Y have 10 observations for each (N=10), and Z has 13 observations (N=13). Each observation should have two digits (such as “83” or “8.3”).

2) Draw a stem-and-leaf display for variable Z only and draw a box plot display for variable Z after specifying the 5 numbers (UEX, LEX, FU, FL, MD).

3) Calculate the mean and standard deviation for variable X

4) Calculate the mean and standard deviation for variable Y

5) In order to predict Y from X, we need to set up a regression equation: (a) Calculate two regression constants (slope and y-intercept) and (b) present the equation.

6) As you have the mean for variable X and Y (from questions 3 and 4 above), once you have the mean for variable Z, can you obtain the mean for the entire data set by computing the mean of the three means? Why or why not? Explain.

Solutions

Expert Solution

####   (1) ####
X=round(rnorm(10,50,5),2)
Y=round(rnorm(10,50,5),2)
Z=round(rnorm(13,50,5),2)
######## (2) ######
stem(Z)

The decimal point is 1 digit(s) to the right of the |

4 | 4
4 | 677899
5 | 02
5 | 668
6 | 0

boxplot(Z)


summary(Z)

    min    1st Qu.Median Mean   3rd Qu. Max.
43.73   47.39   49.06   50.90   55.50   60.05

mean(X)
[1] 49.683
> sd(X)
[1] 5.123309
> ###########(4) #####
> mean(Y)
[1] 50.704
> sd(Y)
[1] 5.522938

######### (5) ####
L=lm(Y~X)
summary(L)

Call:
lm(formula = Y ~ X)

Residuals:
     Min       1Q   Median       3Q      Max
-10.7655 -0.7191   0.0195   2.8518   5.9810

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept) 80.4052    15.8325   5.078 0.000955 ***
X            -0.5978     0.3172 -1.885 0.096175 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.875 on 8 degrees of freedom
Multiple R-squared: 0.3075,    Adjusted R-squared: 0.221
F-statistic: 3.553 on 1 and 8 DF, p-value: 0.09617


Y = 80.4 - 0.59 X

######### (6) ####
> mean(Z)
[1] 50.9
> mean(mean(X), mean(Y), mean(Z))
[1] 49.683


Related Solutions

Suppose X and Y are independent variables and X~ Bernoulli(1/2) and Y~ Bernoulli(1/3) and Z=X+Y A-...
Suppose X and Y are independent variables and X~ Bernoulli(1/2) and Y~ Bernoulli(1/3) and Z=X+Y A- find the joint probability table B- find the probility distribution table of Z C- find E(X+Y) D- find E(XY) E- find Cov(X, Y)
1. You have a mixture of three proteins X, Y, and Z.        X is positively...
1. You have a mixture of three proteins X, Y, and Z.        X is positively charged, has a mass of 100 kDa, it binds sugars.        Y is positively charged, has a mass of 200 kDa, it does not bind sugars.        Z is negatively charged, has a mass of 100 kDa, it does not bind sugars. What will be the most efficient method to purify protein X from the mixture of X, Y, and Z? A. washing B....
Python # Write a program that examines three variables—x, y, and z # and prints the...
Python # Write a program that examines three variables—x, y, and z # and prints the largest odd number among them. # If none of them are odd, it should print a message to that effect. n = input('Enter the 1st Integer x: ') x = int(n) n = input('Enter the 2nd Integer y: ') y = int(n) n = input('Enter the 3rd Integer z: ') z = int(n) if x % 2 == 0 and y % 2 ==...
If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z)...
If X, Y and Z are three arbitrary vectors, prove these identities: a. (X×Y).Z = X.(Y×Z) b. X×(Y×Z) = (X.Z)Y – (X.Y)Z c. X.(Y×Z) = -Y.(X×Z)
The joint density function for random variables X, Y, and Z is f(x, y, z)= Cxyz  if...
The joint density function for random variables X, Y, and Z is f(x, y, z)= Cxyz  if 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2, and f(x, y, z) = 0 otherwise. (a) Find the value of the constant C. (b) Find P(X ≤ 1, Y ≤ 1, Z ≤ 1). (c) Find P(X + Y + Z ≤ 1).
Assume there are three subsets X, Y, Z of some universal set U. | X u...
Assume there are three subsets X, Y, Z of some universal set U. | X u Y u Z | = 41 | X | = 20 | Y | = 28 | Z | = 21 | X n Y | = 12 | X n Z | = 10 |Y n Z | = 11 |X-| = 24 (bar over top of X). Solve: a) | X u Y | b) | Y △ Z | c) |...
[x, y, and z are integer variables, which expressions are equivalent to each other?] a. (x==y...
[x, y, and z are integer variables, which expressions are equivalent to each other?] a. (x==y && x !=z) || (x!=y && x==z) b. (x==y || x==z) && (x!=y || x!=z) c. (x==y) != (x==z)
1.You have three hypothetical (please note, these are not REAL) elements, X, Y, and Z, with...
1.You have three hypothetical (please note, these are not REAL) elements, X, Y, and Z, with the following electronegativity values: X = 0.6 Y = 3.2 Z = 3.5 Please note that X, Y, Z are only placeholders and aren’t referring to an actual specific element on the periodic table. You react the hypothetical elements to form the hypothetical substances XY, XZ, and YZ. Answer the following questions: ● What kind of substance is XY? What kinds of bond is...
Find ??, ?? and ?? of F(x, y, z) = tan(x+y) + tan(y+z) – 1
Find ??, ?? and ?? of F(x, y, z) = tan(x+y) + tan(y+z) – 1
Assume that X, Y, and Z are independent random variables and that each of the random...
Assume that X, Y, and Z are independent random variables and that each of the random variables have a mean of 1. Further, assume σX = 1, σY = 2, and σZ = 3. Find the mean and standard deviation of the following random variables: a. U = X + Y + Z b. R = (X + Y + Z)/3 c. T = 2·X + 5·Y d. What is the correlation between X and Y? e. What is the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT