I see that you have provided an image of a bivariate dataset, which asks for the regression equation for the given data. Let's work through the process.

The dataset you uploaded contains two variables: $X$ (the independent variable) and $Y$ (the dependent variable). To find the regression equation, we typically use the least squares method to compute the line of best fit. The equation of the line is of the form:

$Y = a + bX$

where:

• $b$ is the slope of the line.
• $a$ is the y-intercept.

I will extract the data points and calculate the regression line for you.

Here is the dataset from the image:

• $X: 12, 9, 6, 3, 5, 7, 10, 15$
• $Y: 34.1, 31.5, 29.8, 27.9, 31.4, 30.3, 33.2, 35.4$

Let me calculate the regression equation.The regression equation for the given dataset is:

$Y = 26.78 + 0.59X$

Where:

• The intercept $a = 26.78$
• The slope $b = 0.59$

This means that for every unit increase in $X$, $Y$ increases by approximately 0.59 units.

Do you have any questions or would you like more details on how this was calculated?

Here are 5 related questions you might consider:

1. How is the slope of a regression line interpreted in practical scenarios?
2. How can you determine if this regression line fits the data well?
3. What is the role of residuals in regression analysis?
4. How would you compute the coefficient of determination $R^2$ for this data?
5. Can we use this regression model for predictions outside the given $X$ range?

Tip: Always check the significance of your regression model using statistical tests like the t-test for the slope, or the F-test for the overall model.