Linear Regression by David Spade, PhD

About the Lecture

The lecture Linear Regression by David Spade, PhD is from the course Statistics Part 1. It contains the following chapters:

Linear Regression
The Y-Intercept
Making Predictions
The R-squared Quantity
After Regression

Included Quiz Questions

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?