Quiz For Faculty Trial

1.

A regression analysis is inappropriate when
- A.
  
  You have two variables that are measured on an interval or ratio scale.
- B.
  
  You want to make predictions for one variable based on information about another variable.
- C.
  
  The pattern of data points forms a reasonably straight line
- D.
  
  There is heteroscedasticity in the scatter plot.
Correct Answer
D. There is heteroscedasticity in the scatter plot.

Explanation
Heteroscedasticity refers to the unequal variability of the residuals, or the differences between the observed and predicted values, across the range of the independent variable in a regression analysis. When there is heteroscedasticity in the scatter plot, it violates one of the assumptions of linear regression, which assumes that the residuals have constant variance. This means that the variability of the residuals is not consistent across the range of the independent variable. As a result, the regression analysis may produce inaccurate and unreliable estimates and predictions. Thus, when there is heteroscedasticity in the scatter plot, regression analysis is inappropriate.

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2.

In regression analysis, the variable that is being predicted is;
- A.
  
  The independent variable
- B.
  
  the dependent variable
- C.
  
  Usually denoted by x
- D.
  
  Usually denoted by r
Correct Answer
C. Usually denoted by x

Explanation
In regression analysis, the variable that is being predicted is usually denoted by x. This means that x represents the independent variable, which is the variable that is being used to predict or explain the values of another variable. The dependent variable, on the other hand, is the variable that is being predicted or explained by the independent variable. Therefore, in regression analysis, x is the variable that is being predicted, not the dependent variable.

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3.

The coefficient of determination is
- A.
  
  Simple Linear Regression
- B.
  
  The square root of the correlation coefficient
- C.
  
  Usually less than zero
- D.
  
  Equal to zero
Correct Answer
A. Simple Linear Regression

Explanation
The coefficient of determination is a measure of how well the regression line fits the data points in a simple linear regression model. It represents the proportion of the total variation in the dependent variable that is explained by the independent variable(s). The coefficient of determination is always between 0 and 1, where 0 indicates no relationship between the variables and 1 indicates a perfect fit. Therefore, the correct answer is "Simple Linear Regression."

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4.

Least square method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the _______ deviations
- A.
  
  Vertical
- B.
  
  Horizontal
- C.
  
  Both of these
- D.
  
  None of these
Correct Answer
A. Vertical

Explanation
The least square method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the vertical deviations. This means that it focuses on minimizing the vertical distance between the observed data points and the line of best fit. By minimizing these vertical deviations, the least square method aims to find the line that provides the best overall fit to the data.

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5.

The standard deviation is to the mean as the ____________ is to the regression line
- A.
  
  Z-score
- B.
  
  SSR
- C.
  
  Coefficient of determination
- D.
  
  Standard error of the estimate
- E.
  
  Option 5
Correct Answer
A. Z-score

Explanation
The z-score is a measure of how many standard deviations a particular data point is away from the mean. Similarly, the regression line is a line that represents the relationship between the independent variable(s) and the dependent variable in a regression analysis. The z-score and the regression line both provide information about the relationship between variables and their deviation from the mean or predicted values. Therefore, the z-score is to the mean as the regression line is to the standard error of the estimate.

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6.

Which one of the following is the most appropriate definition of a 99% confidence interval
- A.
  
  99% of the time in repeated samples, the interval would contain the true value of the parameter
- B.
  
  99% of the time in repeated samples, the interval would contain the estimated value of the parameter
- C.
  
  99% of the time in repeated samples, the null hypothesis will be rejected
- D.
  
  99% of the time in repeated samples, the null hypothesis will not be rejected when it was false
Correct Answer
A. 99% of the time in repeated samples, the interval would contain the true value of the parameter

Explanation
A 99% confidence interval means that if we were to take repeated samples from the same population and calculate a confidence interval for each sample, approximately 99% of those intervals would contain the true value of the parameter we are estimating. This means that there is a high level of confidence that the interval we calculate includes the true value.

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7.

A residual is defined as
- A.
  
  The difference between the actual Y values and the mean of Y
- B.
  
  The difference between the actual Y values and the predicted Y values.
- C.
  
  The predicted value of Y for the average X value.
- D.
  
  The square root of the slope
Correct Answer
A. The difference between the actual Y values and the mean of Y

Explanation
A residual is a measure of the difference between the observed values of the dependent variable (Y) and the predicted values of Y. In this case, the correct answer states that a residual is the difference between the actual Y values and the mean of Y. This means that it represents the deviation of each data point from the average value of Y. By calculating and analyzing residuals, we can assess the accuracy and effectiveness of a predictive model.

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Quiz For Faculty Trial

A regression analysis is inappropriate when

In regression analysis, the variable that is being predicted is;

The coefficient of determination is

Least square method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the _______ deviations

The standard deviation is to the mean as the ____________ is to the regression line

Which one of the following is the most appropriate definition of a 99% confidence interval

A residual is defined as