Question

question 3 of 7, step 1 of 1
identify the simple linear regression model.
answer
5/10
correct
options:
$hat{y} = b_0 + b_1 x$
$y = \beta_0 + \beta_1 x + \epsilon$
$y = b_0 + b_1 x + \epsilon$
$hat{y} = b_0 + b_1 x_1 + b_2 x_2$

Explanation:

The simple linear regression model is used to predict the value of a dependent variable ($\hat{y}$) based on the value of an independent variable ($x$). The formula $\hat{y}=b_0 + b_1x$ represents the estimated regression line, where $b_0$ is the y - intercept and $b_1$ is the slope. The other options are incorrect because:

• $y = b_0 + b_1x+\varepsilon$ is the population regression model (not the estimated one as the hat symbol is missing for $\hat{y}$).
• $y=\beta_0+\beta_1x+\varepsilon$ uses population parameters ($\beta$) instead of sample estimates ($b$).
• $\hat{y}=b_0 + b_1x_1 + b_2x_2$ is a multiple linear regression model (has two independent variables $x_1$ and $x_2$).

Answer:

$\hat{y}=b_0 + b_1x$