Question

The sales of a company (in million dollars) for each year are shown in the table below. Is there evidence of a linear relationship between the two variables, and are they positively correlated?

x (years since 2010)	5	6	7	8	9
y (sales in millions)	12	19	29	37	45

                                                       

                                                                        

            a.         Assign variables and sketch the scatter gram (2)

            b.         State the Null and Alternative Hypotheses as if a complete hypothesis test had been conducted. (2)

            c.         Find the linear correlation coefficient. (1)

            d.         At what level is there evidence of linear correlation? (2)

            e.         State the least squares equation and sketch it on the scatter gram. (2)

            f.          Estimate the income in the year 2021 (1)

Answer 1

a) Scatter Plot

b) Null and Alternative Hypothesis:

H0: they are not positively correlated

H1: they are positively correlated

c) From the given data

	X	Y	X^2	Y^2	XY
	5	12	25	144	60
	6	19	36	361	114
	7	29	49	841	203
	8	37	64	1369	296
	9	45	81	2025	405
Total:	35	142	255	4740	1078

From the above table,

c) Test for correlation Coefficient:

Thus we conclude that X and Y are positive correlation

e) From the above table

f) Given Year  = 2021

i.e. X = Year - 2010

= 2021 - 2010 = 11

The prediction income of the year 2021 is

Y-hat = 8.4(11) - 30.4

= 62 sales in millions