SHOW FULL WORK Use the table below Round all answers to four

SHOW FULL WORK!

Use the table below. Round all answers to four decimal places. Find the linear regression equation y = ax + b. Find the coefficient of determination r^2 and interpret. Use the regression equation to predict y when x = 11 and x = 18.

Solution

Let X = education (in years)

Y = income (in thousands)

We can find linear regression equation by using TI - 83 calculator,

steps :

STAT --> ENTER --> ENTER data in L1 and L2 --> STAT --> CALC --> 8 : LinReg(a+bx) --> ENTER --> ENTER

Output :

a = -35.5639

b = 6.1184

y = -35.5639 + 6.1184*x

Find the coeffiient of determination r² and interpret.

STAT --> ENTER --> ENTER data in L1 and L2 --> STAT --> CALC --> 2: 2-Var Stats --> ENTER --> ENTER

Output is as follows :

X = 84, X² = 1084, n1 = 7, Y = 265, Y² = 13817, XY = 3645

r = [n(XY) - (X)(Y) ] / sqrt [ (nX² -(X)²)* (nY² -(Y)²) ]

r = [ (7*3645) - (84*265) / sqrt[ ( (7*1084) - 84² ) *( (7*13817) - 13817² ) ]

r = 3255 / sqrt(532*26494)

r = 3255 / 3754.305

r = 0.8670

r² = 0.8670² = 0.7517 = 0.7517*100 = 75.17%

It expresses the proportion of the variation in Y which is explained by variation in X.

Predict y when x = 11 and x = 18

y = -35.5639 + 6.1184*x = -35.5639 + 6.1184*11 = 31.7385

y = -35.5639 + 6.1184*x = -35.5639 + 6.1184*18 = 74.5673