To find the least-squares regression line for predicting metabolic rate ($y$) from lean body mass ($x$), we use the formula:

$\hat{y} = a + bx$

where:

• $b$ is the slope, calculated by $b = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}$,
• $a$ is the y-intercept, calculated by $a = \bar{y} - b\bar{x}$,
• $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$, respectively.

Given dataTo find the least-squares regression line for predicting metabolic rate ($y$) from lean body mass ($x$), we use the formula:

$\hat{y} = a + bx$

where:

• $b$ is the slope, calculated by $b = \frac{\sum (x - \bar{x})(y - \bar{y})}{\sum (x - \bar{x})^2}$,
• $a$ is the y-intercept, calculated by $a = \bar{y} - b\bar{x}$,
• $\bar{x}$ and $\bar{y}$ are the means of $x$ and $y$, respectively.

Given

• Lean body mass (x): $40.5, 47.8, 49.6, 37.4, 53.9, 48.3, 51.1, 40.1, 43.1, 40.4, 40.5, 47.3$
• Metabolic rate (y): $1010, 910, 1200, 1590, 1280, 1600, 1090, 1300, 1540, 1260, 1340, 1420$

Let's calculate the regression line parameters.The least-squares regression line for predicting metabolic rate ($y$) from body mass ($x$) is:

$\hat{y} = 1746.40 - 10.03x$

Would you like further details on the calculation process or have any questions?

Here are five related questions to consider:

1. How does the slope affect the relationship between body mass and metabolic rate?
2. What would the predicted metabolic rate be for a lean body mass of 45 kg?
3. How would changes in metabolic rate impact predictions if the slope were positive?
4. What is the significance of the y-intercept in the context of this data?
5. How can we interpret the strength of the correlation between body mass and metabolic rate?

Tip: In regression analysis, understanding the units of each variable is key to interpreting the slope accurately.