A certain force x is applied to a wire and the elongation of

A certain force (x) is applied to a wire and the elongation of the wire is recorded (y). The following data were recorded: Find the sum of the Xs. Find the sum of the Ys. Find the sum of the Xs squared. Find the sum of the Ys squared. Find the sum of the XYs. Find S_xx. Find S_xy. Find S_yy. Find the slope of the line of best fit. Find the y intercept. Calculate the estmate of the variance of the error term in the linear regression equation (s^2). Calculate the t-statistic for testing the slope against zero. Does the slope differ significantly (alpha = 0.1) from zero?.

Solution

i)The test statistic is given by t = b₁ / SE

where b₁ is the slope of the sample regression line, and SE is the standard error of the slope.

and SE = s_b1 = sqrt [ (y_i - _i)² / (n - 2) ] / sqrt [ (x_i - x)² ]

Here SE=2.50458

(y_i - _i)²=439.105,(x_i - x)²=17.5,n=6

t=18.1/SE=7.22676