A regression analysis was conducted using a sample of 63 observations. The dependent variable Y was regressed against two independent variables, X1 and X2, yielding the regression equation Y = 76.40 - 6.388X1 + 0.870X2. The standard error of the coefficient for X1 (b1) is 3.453 and the standard error of the coefficient for X2 (b2) is 0.611. Based on a significance level of 0.05, conclusions can be drawn about the relationship between X1 and Y.

1. Using a sample of 63 observations, a dependent variable Y is regressed against two variables X1
and X2 to obtain the fitted regression equation Y = 76.40 - 6.388X1 + 0.870X2. The standard
error of b1 is 3.453 and the standard error of b2 is 0.611. At a = .05, we could:
Solution
Using a sample of 63 observations, two variables X1 and X2 are regressed against a dependent
variable Y yielding the fitted regression equation = 76.40 ? 6.388x1 + .870x2. The standard error
of b1 is 2.453. In a two-tailed test of the hypothesis that b1 = 0 at a = .05, we would conclude
that A) there is a significant direct relationship between X1 and Y. B) there is a significant
inverse relationship between X1 and Y. C) there is insufficient statistical evidence to say that a
relationship exists between X1 and Y D) there is too much Type II error risk to conclude
anything about the relationship.
Answer: Here the sign of the coefficient of x1 is missing. Here the answer depends on the sign of
b1.
If b1 = 6.388, then the correct answer is
A) there is a significant direct relationship between X1 and Y.
If b1 = -6.388, then the correct answer is
B) there is a significant inverse relationship between X1 and Y.