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In: Statistics and Probability

The sales of a company (in million dollars) for each year are shown in the table...

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.

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

c. Find the linear correlation coefficient.

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

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

f. Estimate the income in the year 2021.

Expert Solution

a) Scatter Plot

b) 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

c) Test for correlation Coefficient:

Thus we conclude that X and Y are positive correlation

e) From the given 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

orchestra answered 3 years ago

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The sales of a company (in million dollars) for each year are shown in the table...

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