combine, keep

Question

asked 2021-01-04

Let D be the set of all students at your school, and let M(s) be a ”s is a math major”, let C(s)”s
is a computer science student”, and let E(s) be ”s is an engineering student.” Express each of the following statements using quantifiers, variables, and predicates M(s), C(s) and E(s)

asked 2020-12-25

Case: Dr. Jung’s Diamonds Selection

With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.

After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.

1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?

2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?

3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?

1

6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?

9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

With Christmas coming, Dr. Jung became interested in buying diamonds for his wife. After perusing the Web, he learned about the “4Cs” of diamonds: cut, color, clarity, and carat. He knew his wife wanted round-cut earrings mounted in white gold settings, so he immediately narrowed his focus to evaluating color, clarity, and carat for that style earring.

After a bit of searching, Dr. Jung located a number of earring sets that he would consider purchasing. But he knew the pricing of diamonds varied considerably. To assist in his decision making, Dr. Jung decided to use regression analysis to develop a model to predict the retail price of different sets of round-cut earrings based on their color, clarity, and carat scores. He assembled the data in the file Diamonds.xls for this purpose. Use this data to answer the following questions for Dr. Jung.

1) Prepare scatter plots showing the relationship between the earring prices (Y) and each of the potential independent variables. What sort of relationship does each plot suggest?

2) Let X1, X2, and X3 represent diamond color, clarity, and carats, respectively. If Dr. Jung wanted to build a linear regression model to estimate earring prices using these variables, which variables would you recommend that he use? Why?

3) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

4) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

5) Dr. Jung now remembers that it sometimes helps to perform a square root transformation on the dependent variable in a regression problem. Modify your spreadsheet to include a new dependent variable that is the square root on the earring prices (use Excel’s SQRT( ) function). If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?

1

6) Suppose Dr. Jung decides to use clarity (X2) and carats (X3) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

7) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must actually square the model’s estimates to convert them to price estimates.) Which sets of earring appears to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

8) Dr. Jung now also remembers that it sometimes helps to include interaction terms in a regression model—where you create a new independent variable as the product of two of the original variables. Modify your spreadsheet to include three new independent variables, X4, X5, and X6, representing interaction terms where: X4 = X1 × X2, X5 = X1 × X3, and X6 = X2 × X3. There are now six potential independent variables. If Dr. Jung wanted to build a linear regression model to estimate the square root of earring prices using the same independent variables as before, which variables would you recommend that he use? Why?

9) Suppose Dr. Jung decides to use color (X1), carats (X3) and the interaction terms X4 (color * clarity) and X5 (color * carats) as independent variables in a regression model to predict the square root of the earring prices. What is the estimated regression equation? What is the value of the R2 and adjusted-R2 statistics?

10) Use the regression equation identified in the previous question to create estimated prices for each of the earring sets in Dr. Jung’s sample. (Remember, your model estimates the square root of the earring prices. So you must square the model’s estimates to convert them to actual price estimates.) Which sets of earrings appear to be overpriced and which appear to be bargains? Based on this analysis, which set of earrings would you suggest that Dr. Jung purchase?

asked 2021-01-10

The problem reads: Suppose \(\displaystyle{P}{\left({X}_{{1}}\right)}={.75}\) and \(\displaystyle{P}{\left({Y}_{{2}}{\mid}{X}_{{1}}\right)}={.40}\). What is the joint probability of \(\displaystyle{X}_{{1}}\) and \(\displaystyle{Y}_{{2}}\)?

This is how I answered it. P(\(\displaystyle{X}_{{1}}\) and \(\displaystyle{Y}_{{2}}\)) \(\displaystyle={P}{\left({X}_{{1}}\right)}\times{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}={.75}\times{.40}={0.3}.\)

What I don't understand is how do you get the \(\displaystyle{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}\)? I am totally new to Statistices and I need to understand each part of the process in order to get the whole concept. Can anyone help me to understand why the P and X exist and what they represent?

This is how I answered it. P(\(\displaystyle{X}_{{1}}\) and \(\displaystyle{Y}_{{2}}\)) \(\displaystyle={P}{\left({X}_{{1}}\right)}\times{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}={.75}\times{.40}={0.3}.\)

What I don't understand is how do you get the \(\displaystyle{P}{\left({Y}_{{1}}{\mid}{X}_{{1}}\right)}\)? I am totally new to Statistices and I need to understand each part of the process in order to get the whole concept. Can anyone help me to understand why the P and X exist and what they represent?

asked 2020-10-27

A population of N =16 scores has a mean of p = 20,
After one score is removed from the population, the new mean is found to be \(\displaystyleμ={19}\). What is the value of ine score that was removed? (Hint: Compare the val-
ues for X before and after the score was removed.)

asked 2020-12-01

The circle, ellipse, hyperbola, and parabola are examples of conic sections. Their
quation contains \(x^2 terms, y^2\) terms, or both.
When these terms both appear, are on the same side, and have different coefficients
with same signs, the equation is that of an ellipse.

asked 2020-12-24

Suppose a class consists of 4 students majoring in Mathematics, 3 students majoring in Chemistry and 4 students majoring in Computer Science. How many compositions are possible to form a group of 3 students if each group should consist at most 2 students majoring in Computer Science?

asked 2021-01-04

Suppose a class consists of 5 students majoring in Computer Science, 5 students majoring in Chemistry and 3 students majoring in Mathematics. How many ways are possible to form a group of 3 students if each group should consist at most 2 students majoring in Computer Science?

asked 2020-12-13

A radio station gives a pair of concert tickets to the six caller who knows the birthday of the performer. For each person who calls, the probability is 0.75 of knowing the performer's birthday. All calls are independent.

a) What is the PMF of L, the numberof calls necessary to find the winner? MSK b) What is the probability of finding the winner on the tenth caller?

c) What is the probability of finding the winner on the tenth caller?

a) What is the PMF of L, the numberof calls necessary to find the winner? MSK b) What is the probability of finding the winner on the tenth caller?

c) What is the probability of finding the winner on the tenth caller?

asked 2021-02-05

A radio station gives a pair of concert tickets to the 6th called who knows the birthday of the performer. For each person who calls, the probability is.75 of knowing the performer birthday. All calls are independent.

a. What is the PMF (Probability Mass Function) of L, the number of calls necessary to find the winner?

b. What is the probability of finding the winner on the 10th call?

c. What is the probability that the station will need 9 or more calls to find a winner?

a. What is the PMF (Probability Mass Function) of L, the number of calls necessary to find the winner?

b. What is the probability of finding the winner on the 10th call?

c. What is the probability that the station will need 9 or more calls to find a winner?

asked 2020-11-11

How would adding 50 points to each score affect the mean?