Question

The ages in years of 10 children and the number of words in their vocabulary are shown below.

Age (x) 1 2 3 4 5 6 3 5 2 4

Vocabulary

Size (y) 3 220 540 1100 2100 2600 730 2200 260 1200

Which variable is the dependent variable and which variable is the independent variable?

Using technology, calculate both the correlation value r and the regression equation between these two variables.

Interpret the correlation value r in regards to the relationship between age and vocabulary.

Is the above regression equation a valid regression equation to use to make predictions? In other words does the pattern we see in our sample extend into the entire population? Use a significance level α = .01 and table to determine it's validity.

Predict the vocabulary of a 3.5 year old using your obtained regression line.

  

Answer 1

Ans:

	Age	Vocabulary
1	1	3
2	2	220
3	3	540
4	4	1100
5	5	2100
6	6	2600
7	3	730
8	5	2200
9	2	260
10	4	1200
mean=	3.5000	1095.300
SD=	1.5811	919.1595
r	0.9738
slope,b=	566.1111
y-intercept,a	-886.0889

Regression equation,

Vocabulary=566.111*Age-886.089

There is positive relationship between vocabulary and age.

Test statistic:

t=0.9738*sqrt((10-2)/(1-0.9738^2))

t=12.112

Reject the null hypothesis.

Yes,there is significant relationship between age and vocab,so model is effcective to predict vocab.

Vocubalary=566.111*3.5-886.089=10.95.2