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.

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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
150
170
130
130
80
180
 
​(a)
x=160
calories
​(b)
x=90
calories
​Sodium, y
415
465
350
370
260
520
 
​(c)
x=120
calories
​(d)
x=50
calories
 
 
 

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Part 1
Find the regression equation.
 
y=enter your response herex+​(enter your response here​)
​(Round to three decimal places as​ needed.)
Part 2
Choose the correct graph below.
 
 
A.
 
 
 
 
02000560CaloriesSodium (mg)
 
  •  
  •  
  •  
A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 90 units to the right of and 285 units above the origin; 90 units to the right of and 310 units above the origin; 140 units to the right of and 400 units above the origin; 140 units to the right of and 420 units above the origin; 170 units to the right of and 470 units above the origin; 90 units to the right of and 310 units above the origin. A line rises from left to right and passes through the points (50, 176) and (100, 302). All coordinates are approximate.
 
B.
 
 
 
 
02000560CaloriesSodium (mg)
 
  •  
  •  
  •  
A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 10 units to the right of and 250 units above the origin; 30 units to the right of and 110 units above the origin; 30 units to the right of and 315 units above the origin; 30 units to the right of and 265 units above the origin; 60 units to the right of and 160 units above the origin; 60 units to the right of and 220 units above the origin. A line falls from left to right and passes through the points (0, 194) and (77, 0). All coordinates are approximate.
 
C.
 
 
 
 
02000560CaloriesSodium (mg)
 
  •  
  •  
  •  
A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 60 units to the right of and 160 units above the origin; 110 units to the right of and 80 units above the origin; 110 units to the right of and 270 units above the origin; 120 units to the right of and 315 units above the origin; 130 units to the right of and 365 units above the origin; 140 units to the right of and 420 units above the origin. A line falls from left to right and passes through the points (0, 394) and (157, 0). All coordinates are approximate.
 
D.
 
 
 
 
02000560CaloriesSodium (mg)
 
  •  
  •  
  •  
A scatterplot has a horizontal axis labeled "Calories" from 0 to 200 in increments of 20 and a vertical axis labeled "Sodium (in milligrams)" from 0 to 560 in increments of 40. The following points are plotted: 80 units to the right of and 260 units above the origin; 130 units to the right of and 350 units above the origin; 130 units to the right of and 370 units above the origin; 150 units to the right of and 415 units above the origin; 170 units to the right of and 465 units above the origin; 180 units to the right of and 520 units above the origin. A line rises from left to right and passes through the points (50, 170) and (100, 296). All coordinates are approximate.
Part 3
​(a) Predict the value of y for
x=160.
Choose the correct answer below.
 
 
A.447.039
447.039
 
B.346.399
346.399
 
C.170.279
170.279
 
D.
not meaningful
Part 4
​(b) Predict the value of y for
x=90.
Choose the correct answer below.
 
 
A.270.919
270.919
 
B.170.279
170.279
 
C.346.399
346.399
 
D.
not meaningful
Part 5
​(c) Predict the value of y for
x=120.
Choose the correct answer below.
 
 
A.447.039
447.039
 
B.270.919
270.919
 
C.346.399
346.399
 
D.
not meaningful
Part 6
​(d) Predict the value of y for
x=50.
Choose the correct answer below.
 
 
A.170.279
170.279
 
B.270.919
270.919
 
C.447.039
447.039
 
D.
not meaningful
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