Question

The following table shows the average mathematics and science achievement test scores of eighth-grade students from 12 countries around the world..

Math x	Science, y
525	540
558	535
511	518
531	533
392	420
585	569
476	450
496	538
520	535
582	530
532	552
502	515

(a) Draw a scatter plot using one the following website(s): http://www.alcula.com/calculators/statistics/scatter-plot/ or https://www.meta-chart.com/scatter
(b) Estimate the correlation in words (positive, negative, or no correlation)
(c) Calculate the correlation coefficient, r.
(d) Determine whether r is statistically significant at the 0.01 level of significance.
(e) Determine whether r is statistically significant at the 0.05 level of significance.
(f) Calculate the coefficient of determination, r2.
(g) Interpret the meaning of r2 for the given set of data.
(h) Find the equation of the least-squares regression line, if appropriate.

Answer 1

I am using Excel and the command is

Data > Data Analysis > Regression > Select x, y data > ok

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SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8571
R Square	0.7346
Adjusted R Square	0.7081
Standard Error	22.9209
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14541.2370	14541.2370	27.6782	0.0004
Residual	10	5253.6796	525.3680
Total	11	19794.9167
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	153.3187	69.9325	2.1924	0.0531	-2.5005	309.1379	-2.5005	309.1379
Math x	0.7078	0.1345	5.2610	0.0004	0.4080	1.0075	0.4080	1.0075

Positive

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(c)

(Use Excel function= CORREL(x,y)

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d) r_critical= 0.661 (for )

r = 0.8571 > 0.661

So, Statistically significant

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e) r_critical= 0.532(for )

r = 0.8571 > 0.532

So, Statistically significant

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f) r² = 07346

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g) By varying one unit of x there is 73.46% of variation in y

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h) y = 153.3187 + (0.7078)x