Question

The following data shows the speed gain in reading (in words / minute) (Y) versus the number of weeks of participation in a program of fast reading (x). Ten people participated in the program. Here are the results :
number of weeks (x): 2, 3, 8, 11, 4, 5, 9, 7, 5, 7
speed gain (Y): 21, 42, 102, 130, 52, 57, 105, 85, 62, 90
(a) Estimate the regression coefficients a and b for the linear model Y_i = a + bx_i + ε_i, where ε_i i.i.d. ~ N (0, σ²).
(b) Estimate σ².
(c) Give a bilateral confidence interval for σ² at the 99% level.
(d) Test the b = 0 assumption at the 90% level.
(e) Predict speed gain if a person participates in the program for 10 weeks.

Answer 1

The regression equation is
y= 2.639 + 11.797 x

Predictor	Coef	SE Coef	T	P
Constant	2.639	3.277	0.81	0.444
x	11.797	0.4923	23.96	0.000

S = 4.1454 R-Sq = 98.6% R-Sq(adj) = 98.5%

a) The regression coefficients a and b for the linear model Y_i = a + bx_i + ε_i

are 2.639 and 11.797 respectively.

b) The estimated value of σ² is 4.1454^2=17.1843.