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

The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs is Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories.

Step-by-step explanation:

The equation of the least squares regression line (LSRL) predicting sodium level from the number of calories in beef hot dogs can be determined using the given statistics and the formula for the slope (b) of the LSRL:

b = r (sy/sx)

Where r is the correlation coefficient, sy is the standard deviation of the y-values (sodium levels), and sx is the standard deviation of the x-values (calories).

Given that r = 0.887, sy = 102.43 mg, and sx = 22.64 calories, we can calculate the slope (b):

b = 0.887 (102.43 mg / 22.64 calories) = 4.077 mg/calories

Then, we can use the y-intercept (a) in the equation y = a + bx, where a = y-bar - b*x-bar.

Given that the average sodium level y-bar = 401.15 mg and the average number of calories x-bar = 156.85 calories, the y-intercept (a) will be:

a = 401.15 mg - (4.077 mg/calories * 156.85 calories) = 37.77 mg

Therefore, the equation of the LSRL is:

Sodium Level (mg) = 37.77 mg + 4.077 mg/calories × Calories

Answer 2

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) = (r\sigma_(y))/(\sigma_(x))`

`\beta_(0) = \bar{y} - \beta_(1) \bar{x}`

`\beta_(1) = ((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