Question

# The AudioTex Company is a direct marketer of stereo equipment, personal computers, and other electronic products....

The AudioTex Company is a direct marketer of stereo equipment, personal computers, and other electronic products. AudioTex maintains a web based site, but advertises largely by mailing catalogs to its customers. Orders are taken over the phone and via the internet.    There are no physical stores. The data are for a random sample of 1,000 customers of the company at the end of the previous year. The following are the key variables:

 Dependent Variable: SALES Annual sales in dollars Independent Variables GENDER Dummy Variable      1 = Male        0 = Female OWNHOME Dummy Variable      1 = Yes          0 = No MARRIED Dummy Variable      1 = Married    0 = Not Married INCOME Income of the household in dollars CHILDREN Number of children in the household CATALOGS Number of catalogs sent to the house in the last year

The following is the correlation matrix.

 SALES GENDER OWNHOME MARRIED INCOME CHILDREN CATALOGS SALES 1.0000 GENDER 0.1950 1.0000 OWNHOME 0.3480 0.0844 1.0000 MARRIED 0.4711 0.1161 0.2640 1.0000 INCOME 0.6845 0.2583 0.4494 0.6652 1.0000 CHILDREN -0.2248 -0.1055 -0.0323 0.0098 0.0479 1.0000 CATALOGS 0.4664 0.0874 0.0931 0.1371 0.1779 -0.1135 1.0000

SALES is measured as continuous,   CHILDREN is also measured as continuous.   What is best way to summarize the correlation between them? (choose the best answer)

1)The more children you have in the household, the more product is purchased. The relationship is moderate.

2)The more children you have in the household, the less product is purchased. The relationship is weak.

3)Households with children have average higher sales than households without children.

4)There is little to no relationship between SALES and CHILDREN.

Using the given data table

we get

correlation between Sales and Children = -0.2248

this value is negative and less than -0.5.

So, correlation is inverse or negative and weak

therefore, we can say that with increase in number of children, sales goes down by a small amount as the correlation is very weak.

so, option B is correct

option A is incorrect because there will not be any increase in sales as the correlation is negative

option C is incorrect because we have no evidence about the sales for household with and without children.

option D is incorrect because there is a weak negative correlation.