# Answer true or false to each of the following statements and explain your answers. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.

Question
Modeling
Answer true or false to each of the following statements and explain your answers. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.

2020-10-24
The polynomial regression coefficients can be estimated using the method of least squares, by simply manipulating the variables. Thus, the statement “A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.” is ul(True).

### Relevant Questions

Answer true or false to each of the following statements and explain your answers. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.
a. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations.
b. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.
c. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.
Answer true or false to each of the following statements and explain your answers. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations.
Answer true or false to each of the following statements and explain your answers. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.
a. In multiple linear regression, we can determine whether we are extrapolating in predicting the value of the response variable for a given set of predictor variable values by determining whether each predictor variable value falls in the range of observed values of that predictor.
b. Irregularly shaped regions of the values of predictor variables are easy to detect with two-dimensional scatterplots of pairs of predictor variables, and thus it is easy to determine whether we are extrapolating when predicting the response variable.
a. In using the method of transformations, we should only transform the predictor variable to straighten a scatterplot.
b. In using the method of transformations, a transformation of the predictor variable will change the conditional distribution of the response variable.
c. It is not always possible to fnd a power transformation of the response variable or the predictor variable (or both) that will straighten the scatterplot.
For Questions 1 — 2, use the following. Scooters are often used in European and Asian cities because of their ability to negotiate crowded city streets. The number of scooters (in thousands) sold each year in India can be approximated by the function $$N = 61.86t^2 — 237.43t + 943.51$$ where f is the number of years since 1990. 1. Find the vertical intercept. What is the practical meaning of the vertical intercept in this situation? 2. Use a numerical method to find the year when the number of scooters sold reaches 1 million. (Note that 1 million is 1,000 thousand, so N = 1000) Show three rows of the table you used to support your answer and write a clear answer to the problem.
Which of the following statements is/are correct about logistic regression? (There may be more than one correct answer) Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.
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?
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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?
Mathematical modeling is about constructing one or two equations that represent real life situations. What are these math models used for? Provide at least two equations that can be used in the real world. For example: The equation $$s = 30\ h\ +\ 1000$$ can be used to find your salary given the fact you earn a fixed salary of $1000 per month, plus$30 per hours. Here s represents the total salary and h is the number of hours you worked.