SOLUTION: Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (Each pair of variables has a significant​

Algebra ->  Probability-and-statistics -> SOLUTION: Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (Each pair of variables has a significant​      Log On


   

Question 1150239: Find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line.​ (Each pair of variables has a significant​ correlation.) Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. The caloric content and the sodium content​ (in milligrams) for 6 beef hot dogs are shown in the table below.
calories, X ​Sodium, y
150 415
170 465
120 350
130 380
90 260
190 510




​(a) xequals160 calories
​(b) xequals100 calories
​(c) xequals140 calories
​(d) xequals210 calories
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the linear regression calculator at http://www.alcula.com/calculators/statistics/linear-regression/ was used.

the inputs to this calculator were:

150 415
170 465
120 350
130 380
90 260
190 510

the output from this calculator is:

$$$

the straight line equation is:

y = 2.4421593830334 * x + 50.6940874036.

for the stated inputs, the corresponding values of y based on this equation are shown below: 
calories (x)     sodium (y)    calculated y based on equation.
   150             415            417
   170             465            466
   120             350            344
   130             380            368
   90              260            270
   190             510            515

per the equation:

(a) x equals 160 calories, y = 441 milligrams of sodium.
​(b) x equals 100 calories, y = 295 milligrams of sodium.
​(c) x equals 140 calories, y = 393 milligrams of sodium.
​(d) x equals 210 calories, y = 564 milligrams of sodium.

the calculated numbers have been rounded to the nearest whole number.