Question

10 states comparable in the state size, purchasing power and wealth were selected to investigate the effect of marketing expenditures on sales of televisions. For each state, the marketing expenditure X-thousands of dollars and the sales Y-units sold are shown below:

Marketing expenditure	sales
4.9	27
8.8	42
2.1	16
7.6	35
4.4	33
3.5	28
7.0	40
10.1	43
5.6	35
3.0	21

A marketing expenditure of 5.0 (thousand dollars) is planned for New Jersey. Find the probability that sales will exceed 15.3 units in New Jersey. That is find Pr(y0 > 15.3) when x0 = 5.0. In addition find the predicted sales ŷ0 and then consider the t statistic employed to obtain a prediction interval.

Assuming the data represents 10 observations from a bi-variate normal distribution, and test at the 5 percent level H0: ρ = 0.9 against H1: ρ > 0.9.

Answer 1

Let us first of all try to find the regression equation .

Thus the linear regression is :

where represent the sales and marketing expense respectively.

now when =5

then Sales() =3.1442*5+14.0778

=29.7988

The prbabilty of Y >15.3 at x=5

This will be given by

(29.7988-15.3000)/29.7988

=0.48655

Now we need to perform the hypothesis testing on correlation between x and y

But for that we shall have ot calculate the correlation firstly.

The correlation coefficient is 0.919

Now we have test it against a hypothised value of 0.90