Question

Homework #3-2

a) (Use software for this problem) Four independent samples are collected form four normally distributed populations. The data are:

        Group 1:       12     11     14     10     12     10

        Group 2:       14     12     16     15

        Group 3:       17     18     20     22     23

        Group 4:       10     9       13     13

The SST is equal to 305.68. Conduct a test of the null hypothesis that the group means are equal. Use a 5% significance level.

b) (Use software for this problem) The following pairs of observations were collected.

        X       1       2       3       4       5

        Y       2       6       4       10     15

a.     Plot the values of X and Y. What relationship does the scatter diagram suggest?

b.    Find the least squares line

c.    Find the predicted value for each value of X

d.    Find the residual for each predicted value of Y.

e.    Verify that the sum of the residuals in part e is zero.

Answer 1

a).

One factor ANOVA
	Mean	n	Std. Dev
	11.5	6	1.52	Group1
	14.3	4	1.71	Group2
	20.0	5	2.55	Group3
	11.3	4	2.06	Group4
	14.3	19	4.12	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	246.68	3	82.228	20.91	0.0000129
Error	59.00	15	3.933
Total	305.68	18

H1: At least one pair of population means are different

Calculated F=120.91, P=0.00001 which is < 0.05 level of significance.

The null hypothesis is rejected.

The data indicate there is a significant difference among the three groups.

b).

a).

the plot suggests there is positive relation exists between x and y.

b).

Regression Analysis
	r²	0.840	n	5
	r	0.916	k	1
	Std. Error of Estimate	2.394	Dep. Var.	y
Regression output						confidence interval
variables		coefficients	std. error	t (df=3)	p-value	95% lower	95% upper
Intercept	a =	-1.600
x	b =	3.000	0.757	3.962	.0287	0.590	5.410
ANOVA table
Source	SS	df	MS	F	p-value
Regression	90.000	1	90.000	15.70	.0287
Residual	17.200	3	5.733
Total	107.200	4

Regression line y= -1.6+3.0*x

c).d).e). all the 3 results given in the table.

x	y	Predicted	Residual
1	2.0	1.4	0.6
2	6.0	4.4	1.6
3	4.0	7.4	-3.4
4	10.0	10.4	-0.4
5	15.0	13.4	1.6
		Total	0.0