Find the equation of the regression line for the given data

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.

xCalories, x

150

180

120

130

90

190

Sodium, y

410

460

350

380

250

520

(A)Find the regression equation.?

(Round to three decimal places as needed.)

(a) Predict the value of y for x=170

Choose the correct answer below.

A.168.633

B.459.633

C.386.883

D.not meaningful

(b) Predict the value of y for x=100

Choose the correct answer below.

A. 289.883

B.168.633

C. 386.883

D.not meaningful

(c) Predict the value of y for x=140

Choose the correct answer below.

A.386.883

B.289.883

C.459.633

D.not meaningful

(d) Predict the value of y for x=50

Choose the correct answer below.

A.459.633

B. 289.883

C.168.633

D.not meaningful

xCalories, x	150	180	120	130	90	190		(a) x=170 calories	(b) x=100 calories
Sodium, y	410	460	350	380	250	520		(c)x=140 calories	(d) x=50 calories

Solution

Using technology, we get              
              
slope =    2.425233645          
intercept =    47.38317757          
              
Thus, the regression line is              
              
y^ =    2.425x   + 47.383 [ANSWER]

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a)

Thus, if x =    170
  
Then  
  
y^ =    459.633 [answer]

**********************

b)

Thus, if x =    100  
      
Then      
      
y^ =    289.883   [answer]

*********************

c)

Thus, if x =    140
  
Then  
  
y^ =    386.883 [answer]

********

d)

As x = 50 is not within the range of x values in your sample,

OPTION D: NOT MEANINGFUL.