Regresion

1. Given are five observations for two variables x and y xi yi 1 3 2 7 3 5 4 11 5 14

a. Develop a scatter diagram for these data. b. What does the scatter diagram in part (a) indicate about the relationship between the two variables?
*La relación entre ambas es una muy concreta y aproximada. Por lo que en múltiple R es de 92 %. Por lo que se acepta la Hipótesis nula. Además podemos concluir que tiene una fuerte correlación positiva.

c. Try to approximate the relationship between x and y drawing a straight line through the data. d. Develop the estimated regression equation by computing the values of b0 and b1 using equations :
Y=2.6x+0.2
e. Use the estimated regression equation to predict the value of y when, x =4.
Y=2.6(4) + 0.2 = 10.4 + 0.2
Y = 10.6
The estimated regression equation for (exercise 1) data is: y= .20+2.60x

a. Compute the SSE,SST, and SSR, using the following equations: SSE= (yi-yi)2 SSE = 12.40 SST= (yi-yi)2 SST = 80 SSR= (yi-yi)2 SSR = 67.6 b. Compute the coefficient of correlation r
0.845 = + 0.9192

c. Compute the coefficient of determination r2

r2 = 67.6/80 = 0.845

Consider the following hypothesis test: H0: β1 = 0 Ha: β1 ≠ 0 a. Compute the value of the test statistic.
4.044
b. What is the p value?
0.0272
c. At = .05, what is your conclusion?
RHo
d. What is the rejection rule using the critical value? What is your conclusion?
*Se rechaza la hipótesis nula ya que el P value es menor que alfa .05

2. Given are five observations for two variables x and y xi yi 3 55 12 40 6 55 20 10 14 15 f. Develop a scatter diagram for these data. g. Try to approximate