Question

Question 3

A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.

ANOVA
	df	SS
Regression	3	45.9634
Residual	11	2.6218
Total

	Coefficients	Standard Error
Intercept	0.0136
x1	0.7992	0.074
x2	0.2280	0.190
x3	-0.5796	0.920

1. Write out the estimated regression equation for the relationship between the variables. (1 mark)
2. Compute coefficient of determination. What can you say about the strength of this relationship?            
3. Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance.               
4. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.

Answer 1

ANSWER::

a)

Regression equation:

y^ = 0.0136 + 0.7992 x1 + 0.2280 x2 + (-0.5796) x3

b)

Coefficient of determination, R^2 = SSR/(SSR+SSE)

= 45.9634 / (45.9634+2.6218)

= 0.9460

There is a strong relationship between variables.

c)

df(Regression) =    3

df(residual) = 11

SSR =    45.9634

SSE =    2.6218

MSR = SSR/df(regression) =    15.3211

MSE = SSE/df(residual) =    0.2383

F = MSR/MSE =    64.2812

p-value = F.DIST.RT(64.2812, 3, 11) =    0.0000

As p-value < α Reject the null hypothesis. We can conclude that y is significantly related to the independent variables.

d)

Test statistic = -0.5796/0.920 = -0.63

p-value = T.DIST.2T(ABS(-0.63), 11) = 0.5416

As p-value > 0.05, so we fail to reject the null hypothesis. x3 and y are not significantly related.

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