Linear Regression
Über den Vortrag
Der Vortrag „Linear Regression“ von David Spade, PhD ist Bestandteil des Kurses „Statistics Part 1“. Der Vortrag ist dabei in folgende Kapitel unterteilt:
- Linear Regression
- The Y-Intercept
- Making Predictions
- The R-squared Quantity
- After Regression
Quiz zum Vortrag
Which of the following is not true of the linear model?
- The line represented by the linear model goes through every data point.
- The linear model is the equation of a straight line that goes through our data.
- The linear model can be used to model the relationship between two quantitative variables.
- A line with a good fit will have small residuals.
- The linear model cannot be used for qualitative variables.
Which of the following is not true of the relationship between linear regression and correlation?
- The slope of the regression line is equal to the correlation.
- Correlation can, in many cases, give insight into how well the linear model will fit our data.
- We must be careful in using correlation to describe how well the linear model will fit our data.
- Correlation tells us whether the slope of the regression line is positive or negative.
- The intersection of the y-axis does not provide meaningful information about correlation.
Suppose the variables X and Y are linearly related through the regression equation Y= 12.5 - 0.275 X. What do we know from this equation?
- For a one-unit increase in the value of X, we expect a decrease of 0.275 units in the value of Y.
- For a one-unit increase in the value of X, we expect an increase of 0.275 in the value of Y.
- For a one-unit increase in the value of X , we expect a 12.5 unit increase in the value of Y .
- If Y = 0, then X = 12.5.
- For a one-unit decrease in the value of X, we expect a decrease of 0.275 units in the value of Y.
Which of the following is not true of the R² quantity?
- High values of R² mean that the changes in the value of X cause the changes in the value of Y.
- The R² quantity can be used to assess how well the line fits the data in many cases.
- The R² quantity provides the percentage of variation in the response variable that is explained by the regression on the explanatory variable.
- The R² quantity is calculated by squaring the correlation.
- R² ranges from 0 to 1.
What defines the residual value of a regression line?
- The vertical distance from the observed value to the regression line
- The horizontal distance from the observed value to the regression line
- The vertical distance from the expected value to the regression line
- The horizontal distance from the expected value to the regression line
- The lateral distance from the expected value to the regression line
Suppose the relationship between age and earnings could be represented by the linear regression equation Earnings = 100 + 0.8*Age. What would be the estimated earnings of a person whose age is 43?
- 134.4
- 30
- -34.4
- 34.4
- 100
Suppose the relationship between age and earnings could be represented by the linear regression equation Earnings = 100 + 0.8*Age. The actual earnings of a person aged 43 are $150. What is the residual error?
- 15.6
- 0
- -15.6
- 34.4
- 100
Suppose the correlation between two variables is 0.75, standard deviation of y variable is 5 and the standard deviation of x variable is 2.5. What is the slope of the regression line?
- 1.5
- 0
- 1
- 0.375
- 0.75
Suppose the slope of regression line is 2 and Y variable is 10 when X variable is 3. What is the value of the intercept of the regression equation?
- 4
- 0
- 1
- 2
- 3
If a rise in health expenditure leads to a positive linear rise in GDP, then which regression equation is likely to represent their relationship?
- GDP = 100 + 0.9* Health expenditure
- GDP = 100 – 0.9* Health expenditure
- GDP = 100 + 0.9* Health expenditure + 0.23* Health expenditure²
- Health expenditure = 100 – 0.9*GDP
- Health expenditure = 100 + 0.9*GDP
Dozent des Vortrages Linear Regression
David Spade, PhD
Dr. David Spade is an Assistant Professor of Mathematical Sciences and Statistics at the University of Wisconsin-Milwaukee and holds a courtesy appointment as an Assistant Professor of Statistics at the University of Missouri-Kansas City, USA.
He obtained his MS in Statistics in 2010 and then completed his PhD in Statistics from Ohio State University in 2013.
An experienced mathemathics instructor, Dr. Spade has been teaching diverse statistics courses from the introductory to the graduate level since 2007.
Within Lecturio, he teaches courses on Statistics.
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