What is the intention of a simple linear regression?
- to develop a model that can be used to predict the value of Y, given X
To compute?
- the general format of the relationship between two variables, denoted as Y and X
To compute?
- the estimated model (using Excel/PHStat) is generally presented as:
- where values b0 and b1 are taken from the output and provides the estimated coefficients
What is β0?
- the intercept term, which is estimated using the value of b0
- denotes that the expected value of Y is X is equal to zero
What is β1?
- the slope term which is estimated using the value of b1
- this gives us the marginal change in the expected value of Y for a unit change in X
- if β1 is positive, then the line slopes upward
- if β1 is negative, then the line slopes down
(that is, increasing X by one unit results in Y decreasing)
What does the standard error of the estimate do?
- estimates the standard deviation of the errors, or, equivalently, the standard deviation of the possible Y-values associated with any particular X-value
What does the coefficient of determination do?
- provides the proportion of the variation in Y that is explained by the linear model containing X as an explanatory variable
What do we use the estimated model for?
- to predict the value of Y, given X
- need to substitute the value of X with the correct units used to the estimated equation
How can we test the significance of the relationship between Y and X?
- using a t-test
What are the dependent and independent variables for this study? State and report the regression model.
What information does the coefficient b1 in the regression equation provide about the relationship between examination grade and study hours?
Test the null hypothesis that the slope of the regression line is zero.
Use 5% level of significance.
Interpret the result of your test.
Test the null hypothesis that the true regression coefficient is less than or equal to zero.
Use 5% level of significance.
Interpret the result of your test.
Estimate the examination grade of a student who devoted 30hr of study to course preparation.
Report and interpret the value of the coefficient of determination.
The coefficient of determination, R2 = 0.74.
This implies that 74% of the variation in examination grade can be explained by the number.
