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To find the equation of the least squares regression line, we need to use the provided data of "Dosage" (\(x\)) and the corresponding "Rise in blood sugar level" (\(y\)).

The general form of the least squares regression line is:
\[
y = mx + b
\]
where:
- \(m\) is the slope,
- \(b\) is the y-intercept.

To calculate the slope (\(m\)) and intercept (\(b\)) for the least squares regression line, we use the following formulas:

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]
\[
b = \frac{\sum y - m(\sum x)}{n}
\]
where \(n\) is the number of data points.

The data provided is:

| Dosage (\(x\)) | Rise in blood sugar level (\(y\)) |
|----------------|----------------------------------|
| 29             | 29                               |
| 44             | 26                               |
| 60             | 28                               |
| 75             | 17                               |
| 76             | 23                               |
| 85             | 21                               |

Let's proceed to calculate the regression line equation. I'll perform the calculations now.The equation of the least squares regression line is:

\[
y = -0.166x + 34.199
\]

where:
- The slope \(m\) is approximately \(-0.166\),
- The y-intercept \(b\) is approximately \(34.199\).

Would you like further details or have any questions?

Here are some related questions for further exploration:
1. How can you interpret the slope in this context?
2. What does the y-intercept signify in this study?
3. How can you use this equation to predict blood sugar levels for different dosages?
4. What are the assumptions behind using a linear regression model?
5. How can you assess the accuracy of this regression model?

**Tip:** When interpreting the slope, a negative value indicates that as the dosage increases, the rise in blood sugar level tends to decrease.

Find the equation for the least squares regression line of the data described below. The table contains dosage (x) and the rise in blood sugar level (y) data points.

Find the least squares regression line for a dataset involving dosage and blood sugar levels. Learn the process of calculating slope (m) and intercept (b) using key formulas. This example is perfect for high school students learning about linear regression and algebra.

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