Question

We have a dataset with n = 10 pairs of observations (Li, Yi), and n I ti = 683, yi = 813, i=1 i=1 > z* = 47,405, { xiyi = 56,089, L y = 66, 731. i=1 What is an approximate 95% confidence interval for the intercept of the line of best fit?

Answer 1

Answer:

Presently we have,

y = a + bx ------------------------->(1)

Σy = na + bΣx ------------------->(2)

Σxy = aΣx + bΣx^2 ------------>(3)

Now from condition no. (2)

813 = 10a + b*683

10a + 683 b = 813 -----------> (4)

From condition no. (3)

56089 = a 683 + b 47405

683a + 47405b = 56089 ________ (5)

Tackling conditions no. (4) and (5)

then we get

a = 30.6147 and b = 0.742

From condition no. (1)

y = 30.6147 + 0.742 x

substitute xo = 90 in above equation

y = 30.6147 + 0.742 * 90

yo = 97.3947

yo = 97.3947 at xo=90