Linear regression Can you interpret the meaning of the y intercept, b0 and the s

Question

Linear regression
Can you interpret the meaning of the y intercept, b0 and the slope of b1 in the problem? Is the slope statistically different? Why or why not?
Use the linear equation from the output to predict the mean 2015 GDP per capita for a GDP per labor hour of 40.
Indicate the coefficient of determinatio, r^2, and interpret its meaning. Can you interpret the meaning of the y intercept, b0 and the slope of b1 in the problem? Is the slope statistically different? Why or why not?
Use the linear equation from the output to predict the mean 2015 GDP per capita for a GDP per labor hour of 40.
Indicate the coefficient of determinatio, r^2, and interpret its meaning. 0 1 Country 2015 GDP P 2015 GOP Per Labor Hour 2 Australia 44,430.70 3 Austria 42,784.1053.5 4 Belgium 40,097.60 5 Canada 42,227.10 48.5 6 Chile 20,76590 24.2 7Czech Rep 29,07880 33.7 8 Denmark 43,554.70 61.9 9 Estonia 25,40980 28.9 10 Finland 37,443.80 50.1 1 France 36,789.10 60.6 2 Germany 42,932.40 59.5 13 Greece24,225.80 32.2 14 Hungary 24,089 90 31.3 5 Ireland 58,493.50 78.4 16 Israel 31,152 20 17 Italy Chart Title SUMMARY OUTPUT Regression Stotistics Multiple R 09032 R Square 0.81577 Adjusted F 0.80942 Standard 1 624104 Observati F gnificance F 0 Regression Residual 1 5E+09 SE+09 128416 3.6E-12 29 1.1E+09 39E+07 35 0 6.1E+09 coefficientsandard Em t Stat p.value tower 95% upper 95%ower 95 o.oper 95.0 Intercept 1265 59 34313 0.36884 071493 -5752.21 8283.39 -5752.21 8283.39 2015 GDP 77186 68.1128 11.3321 3.6E-12 632 553 911.166 632 553 911.166 Japan 35,19680 39.7 19 Korea34,414.70 $18 20 Latvia 22015so 25.7 1 Luxembou 87,816 20 81.7 2 Mexico 16,419.60 18.5 23 Netherlan 45,610 70 61.8 24 Norway 60,109.00 79.8 25 Portugal 26.26060 318 26 Slovak Re 27,616.90 37.7 27 Slovenia 28,014 20 364 28 Spain 32,098.60 47.7 29 Sweden 44,247.8056 0 Switzerlar 52,186 3054.9 1 United Kir 38,608.90 48.5 12 United Sta $1,592.30 629

Explanation / Answer

Here from the last table we see the coefficients first. We see that the intercept is 1265.59 and the slope coeffcient is 771.86 which basically means that for an increase in 1 unit of GDP per labor hour, there should be an increase in 771.86 units in the mean 2015 GDP per capita.

With the given equation, the prediction of mean 2015 GDP per capita for a GDP per labor hour of 40. would be given as:

= 1265.59 + 771.86*40 = 32139.99

Therefore 32139.99 is the required value of the predicted mean 2015 GDP per capita per labour

Now from the first table we obtain, R2 = 0.81577 which is the coefficient of determination. This basically signifies that there is a significant linear relationship between the dependent and the independent variable.

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