Question

Twenty types of beef hot dogs were tested for calories and sodium content (mg). the hot dogs average 156.85 calories with a standard deviation of 22.64, and the sodium level average 401.15 mg with a standard deviation of 102.43 mg. the correlation given as r = 0.887. the equation of the lsrl predicting sodium level from number of calories is:________

Answer 1

Answer:

y = -228.29 + 4.013x

Step-by-step explanation:

Defining

x: Quantity of calories in the beef hot dogs

y: Content of sodium in the beef hot dogs

The least squares regression line equation is:

$y = \beta_{0} + \beta_{1}x$

Where

$\beta_{1} = \frac{r\sigma_{y}}{\sigma_{x}}$

$\beta_{0} = \bar{y} - \beta_{1} \bar{x}$

$\beta_{1} = \frac{(0.887)(102.43)}{(22.64)}$

$\beta_{1} = 4.013$

$\beta_{0} = 401.15 - (4.013)(156.85)$

$\beta_{0} = -228.29$

Then the regression’s equation is:

y = -228.29 + 4.013x