Question

The following data give information on the ages (in years) and the number of breakdowns during the past month for a sample of machines at a large company. Age(years) 1 4 6 10 12 15 19 Number of CO 1 1 3 5 5 9 breakdowns Find the least squares regression line equation in form y = a + bx .Use "Age” as the independent variable and ”Number of breakdowns” as the dependent variable. Round your answers to two decimal places. û = +

Answer 1

Lease square regression equation.

$\hat{y}$ = b₀ + b₁ *x

b₀ is Intercept , we can find intercept using excel function =INTERCEPT( Y data set column range, x data set column range )

b₁ is Slope , we can find slope using excel function =SLOPE( Y data set column range, x data set column range )

Age Breakdowns 21 =INTERCEPT(B2:38,A2:A8) |-1.18 =SLOPE(B2:38,A2:A8) 0.48

$\hat{y}$ = -1.18 + 0.48 x

Similarly we can find correlation coefficient r using the function =CORREL( y, x )

11 Age Breakdowns minino =CORREL(B2:38,A2:A8) 10.97 7 15 8 19

r = 0.97

Therefore coefficient of determination r² = 0.97*0.97

r² = 0.94