For this discussion, we are going to look at data that should follow a linear relationship....

For this discussion, we are going to look at data that should follow a linear relationship.

1. Begin by gathering data that interests you.

- You can look online, in the newspaper, conduct an experiment yourself… Be creative!

2. What variables did you choose to explore?

- Which is the explanatory variable and which is the response variable? Fully explain why.

3. Describe how you obtained your data.

(Since I'm only allowed about 3 questions per post, this would be part 1 of the question, so if the answer you get seems open-ended/incomplete, it's because it is. But that's fine)

Solutions

Expert Solution

1. The data that interests me and has a roughly linear relationship is the population of China for over 9 years. I have collected data online.

X	Y
Year	Population (millions)
2008	1328.02
2009	1334.5
2010	1340.91
2011	1347.35
2012	1354.01
2013	1360.72
2014	1367.82
2015	1374.62
2016	1382.71
2017	1390.08

2. Explanatory variable is Year

The response variable is the population of China

as with increasing year, the population is increasing thus year is explaining the population.

3. The data is available online.

I have also performed regression analysis in excel to help understand the relation between them

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.999434295
R Square	0.99886891
Adjusted R Square	0.998727524
Standard Error	0.741821775
Observations	10

ANOVA
	df	SS	MS	F	Significance F
Regression	1	3887.769644	3887.77	7064.824	4.47758E-13
Residual	8	4.402396364	0.5503
Total	9	3892.17204

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-12457.18964	164.3648449	-75.7899	1.02E-12	-12836.21565	-12078.16362
Year	6.864727273	0.081671889	84.05251	4.48E-13	6.676391558	7.053062987

The rehression equation is given by

Thus we can say for one unit increase in the year the population increases by 6.864 millions. The coefficient of determination is 0.998 which implies 99.8% variation in the population is explained by year.

please like the solution if it helps you. Thank you.

orchestra answered 1 year ago

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