Question

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.

font size decreased by 1 font size increased by 1 Calories comma xCalories, x	150150	170170	130130	120120	9090	190190		​(a) xequals=160160 calories	​(b) xequals=100100 calories
​Sodium, y	410410	460460	340340	380380	290290	510510		​(c) xequals=140140 calories	​(d) xequals=210210 calories

Find the regression equation.

ModifyingAbove y with caretyequals=nothingxplus+​(nothing​)

​(Round to three decimal places as​ needed.)

Answer 1

Sum of X = 850
Sum of Y = 6084
Mean X = 141.6667
Mean Y = 1014
Sum of squares (SS_X) = 6483.3333
Sum of products (SP) = 44700

Regression Equation = ŷ = bX + a

b = SP/SS_X = 44700/6483.33 = 6.895

a = M_Y - bM_X = 1014 - (6.89*141.67) = 37.265

ŷ = 6.895X + 37.265