Simple Regression Line

发表于 作者 ancydy

For 12.8(p481)

Define dollars spend on advertising as x asix and total sales as y asix.

X Y X^2 X*Y N
12.5 148 156.25 1850 8
3.7 55 13.69 203.5
21.6 338 466.56 7300.8
60 994 3600 59640
37.6 541 1413.76 20341.6
61 89 3721 5429
16.8 126 282.24 2116.8
41.2 379 1697.44 15614.8
254.4 2670 11350.94 112496.5
SSxy 27590.5
SSxx 3261.02
b1 8.460696347
b0 64.69985618

So,the equation of the simple regression line to predict sales from advertising expenditures is Y=64.7+8.46*Y

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Equation of the regression line of GDP and Fertility.

Define Total Fertility Rate as X asix and GDP Per Capita as Y asix.

X Y X^2 X*Y N
2.10 9.7 4.41 20.37 10
5.97 1.5 35.6409 8.955
1.59 37.3 2.5281 59.307
1.30 7.4 1.69 9.62
1.84 16.6 3.3856 30.544
2.01 52.8 4.0401 106.128
1.80 3.8 3.24 6.84
2.35 13.6 5.5225 31.96
0.85 4.1 0.7225 3.485
4.09 2.5 16.7281 10.225
23.90 149.3 77.9078 287.434
SSxy -69.393
SSxx 20.7868
b1 -3.338320473
b0 22.90858593

So,the equation of the simple regression line to Total Fertility Rate from GDP Per Capita is Y=22.9-3.34*X

Pearson Correlation Coefficient For Fertility-GDP data

发表于 作者 ancydy

I difine Total Fertility Rate as X and GDP Per Capita as Y.And calculate the Pearson Correlation Coefficient for it.

R is about -0.299.So Fertility Rate is low negative correlation to the GDP Per Capita.

X Y X^2 Y^2 X*Y N
1 2.10 9.7 4.41 94.09 20.37 10
2 5.97 1.5 35.6409 2.25 8.955
3 1.59 37.3 2.5281 1391.29 59.307
4 1.30 7.4 1.69 54.76 9.62
5 1.84 16.6 3.3856 275.56 30.544
6 2.01 52.8 4.0401 2787.84 106.128
7 1.80 3.8 3.24 14.44 6.84
8 2.35 13.6 5.5225 184.96 31.96
9 0.85 4.1 0.7225 16.81 3.485
10 4.09 2.5 16.7281 6.25 10.225
SUM 23.90 149.3 77.9078 4828.25 287.434
R NUMERATOR -69.393
R DENOMINATION 232.4415439
R -0.2985395761

Scatter Plot of Fertility and GDP

发表于 作者 ancydy

I record 10 countries’ Total Fertility rate and  GDP-Per Capita from  CIA World Factbook’s  Fertility-GDP data .

I make a scatter plot by these data.Plot Fertility on the x-axis and GDP on the y-axis.

DATA of 10 Countries

Country GDP Per Capita Total Fertility Rate
Turkmenistan 9.7 2.10
Uganda 1.5 5.97
UK 37.3 1.59
Ukraine 7.4 1.30
Uruguay 16.6 1.84
US 52.8 2.01
Uzbekistan 3.8 1.80
Venezuela 13.6 2.35
Vietnam 4.1 0.85
Yemen 2.5 4.09

Scatter Plot