1What is the main objective of simple linear regression?
To establish if there is a statistically significant relationship between an input variable and an output variable, and to predict new observations.
2What type of values does the predicted variable in simple linear regression have?
Numerical or continuous values.
3What does simple linear regression aim to minimize?
The overall modeling error by fitting a line to the observed data.
4What is the independent variable usually denoted as?
X.
5What is the dependent variable usually denoted as?
Y.
6What is the purpose of the error term in simple linear regression?
It is the residual between the observed value and the predicted value that lies on the regression line.
7What is the general form of the linear equation in simple linear regression?
y = B₀ + B₁X + e, where B₀ is the y-intercept, B₁ is the slope, X is the independent variable, and e is the error term.
8How do you assess if a predictor variable is statistically significant?
By checking if the p-value is less than 0.05.
9What does an R-square value indicate?
It measures how much of the variability in the output variable is explained by the input variable.
10What is the adjusted R-square value?
It accounts for the proportion of variation explained by the predictor, adjusted for the number of predictors used in the model.
11What was the predicted salary for a candidate with 5 years of experience in the given example?
K73,545.90.
12What does the slope in a simple linear regression model represent?
The change in the dependent variable for every one-unit increase in the independent variable.
13What is the significance of the constant in a linear regression model?
It is the y-intercept, representing the predicted value when the independent variable is zero.
14What is the p-value used for in a simple linear regression model?
To test the statistical significance of the predictors or the overall model.
15What happens when the adjusted R-square value is close to 1?
It indicates that the model explains a high proportion of the variability in the dependent variable.
16What does the line-of-best-fit do in simple linear regression?
It minimizes the total error between the observed values and the predicted values.