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# Identify which assumption is needed to use the linear regression model to make inferences about the relationship. Identify which assumption is the least critical.

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Sampling distributions
asked 2020-10-21
Identify which assumption is needed to use the linear regression model to make inferences about the relationship.
Identify which assumption is the least critical.

## Answers (1)

2020-10-22
Assumptions:
- Data are collected randomly.
- A linear relationship between dependent variable y and explanatory variable x in the population.
- The population values of y at each value of x follow a normal distribution with the same standard deviation at each x value.
In this case, the third assumption is the least critical because the estimates from the regression models have bell-shaped sampling distributions when the sample size is large according to the central limit theorem.

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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?
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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?
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Question 3 options:
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The word Central within its name, is meant to signify its role of central importance in the mathematics of probability and statistics.
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3. The word Central within its name, is meant to signify its role of central importance in the mathematics of probability and statistics.
4. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to 50\%.
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6. The accuracy of the approximation it provides, improves as the sample size n increases.
7. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.
8. It is a special example of the particular type of theorems in mathematics, which are called limit theorems.
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2. It specifies the specific mean of the curve which approximates certain sampling distributions.
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7. The word Central within its name, is mean to signify its role of central importance in the mathematics of probability and statistics.
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