Question

Find the regression​ equation, letting the first variable be the predictor​ (x) variable. Find the best predicted Nobel Laureate rate for a country that has 78.2 Internet users per 100 people. How does it compare to the​ country's actual Nobel Laureate rate of 1 per 10 million​ people?

Internet Users Per 100   Nobel Laureates
79.5   5.5
80.6   24.2
77.8   8.7
45   0.1
82.7   6.1
37.9   0.1
89.2   25.3
88.9   7.6
79.8   9
83.6   12.8
52.8   1.9
77.3   12.7
56.5   3.3
78.4   1.5
92.1   11.5
93.9   25.3
64.6   3.1
57.5   1.9
67.8   1.7
93.4   32.1
84.5   31.6
86.8   18.9
77.6   10.9

Answer 1

using excel>data >data analysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.701503
R Square	0.492106
Adjusted R Square	0.467921
Standard Error	7.455134
Observations	23
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1130.88	1130.88	20.34724	0.000192
Residual	21	1167.16	55.57903
Total	22	2298.039
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-23.1714	7.75977	-2.9861	0.007042	-39.3087	-7.03409
Internet Users Per 100	0.456395	0.101179	4.510791	0.000192	0.245983	0.666808

the regression​ equation is

Nobel Laureate rate = -23.1714 + 0.456395 * Internet users per 100

the best predicted Nobel Laureate rate for a country that has 78.2 Internet users per 100 people is = -23.1714 + 0.456395 * 78.2

= 12.52