the value of the y - intercept a in the least squares regression line $hat{y}=a + bx$ is computed using the…

the value of the y - intercept a in the least squares regression line $hat{y}=a + bx$ is computed using the formula below.\na = $\bar{y}-b\bar{x}$\nuse the previously computed values $\bar{y}=642.66$, $b = 14.822873$, and $\bar{x}=10.3$ to compute a, rounding the result to three decimal places.\na = $\bar{y}-b\bar{x}$\n= 642.66 - ( )10.3\n=\nenter the equation of the least squares regression line for the median six - minute walk distance using representative age, rounding the results to three decimal places.\n$hat{y}=$ + ( )x

the value of the y - intercept a in the least squares regression line $hat{y}=a + bx$ is computed using the formula below.\na = $\bar{y}-b\bar{x}$\nuse the previously computed values $\bar{y}=642.66$, $b = 14.822873$, and $\bar{x}=10.3$ to compute a, rounding the result to three decimal places.\na = $\bar{y}-b\bar{x}$\n= 642.66 - ( )10.3\n=\nenter the equation of the least squares regression line for the median six - minute walk distance using representative age, rounding the results to three decimal places.\n$hat{y}=$ + ( )x

Answer

Explanation:

Step1: Substitute values into formula

We are given $\bar{y}=642.66$, $b = 14.822873$, and $\bar{x}=10.3$. Substitute into $a=\bar{y}-b\bar{x}$. So $a = 642.66-(14.822873)\times10.3$.

Step2: Perform multiplication

$14.822873\times10.3 = 152.6756919$.

Step3: Perform subtraction

$a=642.66 - 152.6756919=489.9843081$. Rounding to three - decimal places, $a\approx489.984$. The least - squares regression line is $\hat{y}=a + bx$. Substituting $a\approx489.984$ and $b = 14.823$ (rounded to three decimal places) we get $\hat{y}=489.984+(14.823)x$.

Answer:

$a = 489.984$; $\hat{y}=489.984+(14.823)x$