(b) find the equation of the least - squares regression line.\nfor the least squares regression line…

(b) find the equation of the least - squares regression line.\nfor the least squares regression line $hat{y}=a + bx$, the slope $b$ is calculated using the equation below.\n$b=\frac{sum(x - \bar{x})(y - \bar{y})}{sum(x - \bar{x})^2}$\nrefer to the data below.\n| age group | representative age (midpoint of age group) | median six - minute walk distance (meters) |\n| ---- | ---- | ---- |\n| 3 - 5 | 4.0 | 541.3 |\n| 6 - 8 | 7.0 | 582.0 |\n| 9 - 11 | 10.0 | 665.3 |\n| 12 - 15 | 13.5 | 699.1 |\n| 16 - 18 | 17.0 | 725.6 |\ncalculate $\bar{x}$ and $\bar{y}$.\n$\bar{x}=square$\n$\bar{y}=square$

(b) find the equation of the least - squares regression line.\nfor the least squares regression line $hat{y}=a + bx$, the slope $b$ is calculated using the equation below.\n$b=\frac{sum(x - \bar{x})(y - \bar{y})}{sum(x - \bar{x})^2}$\nrefer to the data below.\n| age group | representative age (midpoint of age group) | median six - minute walk distance (meters) |\n| ---- | ---- | ---- |\n| 3 - 5 | 4.0 | 541.3 |\n| 6 - 8 | 7.0 | 582.0 |\n| 9 - 11 | 10.0 | 665.3 |\n| 12 - 15 | 13.5 | 699.1 |\n| 16 - 18 | 17.0 | 725.6 |\ncalculate $\bar{x}$ and $\bar{y}$.\n$\bar{x}=square$\n$\bar{y}=square$

Answer

Explanation:

Step1: Calculate the mean of (x) values

The (x) - values are (4.0,7.0,10.0,13.5,17.0). The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}), where (n = 5), (\sum_{i=1}^{5}x_{i}=4.0 + 7.0+10.0 + 13.5+17.0=51.5). So (\bar{x}=\frac{51.5}{5}=10.3).

Step2: Calculate the mean of (y) values

The (y) - values are (541.3,582.0,665.3,699.1,725.6). The formula for the mean (\bar{y}=\frac{\sum_{i = 1}^{n}y_{i}}{n}), where (n = 5), (\sum_{i=1}^{5}y_{i}=541.3+582.0 + 665.3+699.1+725.6=3213.3). So (\bar{y}=\frac{3213.3}{5}=642.66).

Answer:

(\bar{x}=10.3), (\bar{y}=642.66)