## Addendum to Data Visualization posts #21 and #22

In data visualization posts #21 and #22, I referred to the results of simple multivariate linear regressions where I examined the statistical relationships between the cost of electricity across European Union countries and the market penetration of renewable energy sources, and a cost-of-living index. Here are the regression results that form the source data for the predictive plots in those blog posts.

First, with the price of electricity as the dependent variable (DV):

```## Here is the R code for the linear regression (using the generalized linear models (glm) framework:
glm.1<-glm(Elec_Price~COL_Index+Pct_Share_Total,data=eu.RENEW.only,family="gaussian")  # Electricity Price is DV

MODEL INFO:
Observations: 28
Dependent Variable: Price of Household Electricity (in Euro cents)
Type: Linear regression

MODEL FIT:
χ²(2) = 306.82, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.40
AIC = 166.04, BIC = 171.37

Standard errors: MLE
-------------------------------------------------------------
Est.   S.E.   t val.      p
------------------------------ ------ ------ -------- ------
(Intercept)                     4.10   3.59     1.14   0.26
Cost-of-Living Index            0.22   0.06     3.59   0.00
Renewables (% share of total)   0.03   0.04     0.74   0.46
-------------------------------------------------------------```

We can see that the cost-of-living index is positively correlated with the price of household electricity, and it is statistically significant at conventional (p=0.05) levels. The market penetration of renewables (on the other hand) is not statistically significant (once controlling for cost-of-living.

Now, we use the pre-tax price of electricity (there are large differences in levels of taxation of household electricity across EU countries) as the DV. Here are the regression code (R) and the model results of the multivariate linear regression.

```## Here is the R code for the linear regression (using the generalized linear models (glm) framework:

glm.2<-glm(Elec_Price_NoTax~COL_Index+Pct_Share_Total,data=eu.RENEW.only,family="gaussian")  # Elec Price LESS taxes/levies is DV

MODEL INFO:
Observations: 28
Dependent Variable: Pre-tax price of Household Electricity (Euro cents)
Type: Linear regression

MODEL FIT:
χ²(2) = 100.13, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.44
AIC = 130.11, BIC = 135.43

Standard errors: MLE
-------------------------------------------------------------
Est.   S.E.   t val.      p
-----------------------------  ------- ------ -------- ------
(Intercept)                      5.20   1.89     2.75   0.01
Cost-of-Living Index             0.14   0.03     4.41   0.00
Renewables (% share of total)   -0.03   0.02    -1.44   0.16
-------------------------------------------------------------```

Here, we see an even stronger relationship between the cost-of-living and the pre-tax price of household electricity, while there is (once the cost-of-living is controlled for) a negative (though not quite statistically significant) relationship between the pre-tax cost of electricity and the market penetration of renewables across EU countries.

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## Data Visualization #22—EU Electricity Prices (Part II)

In post #21 of this series, I examined the relationship between electricity prices across European Union (EU) countries and the market penetration of renewable (solar and wind) energy sources. There’s been some discussion amongst the defenders of the continued uninterrupted burning of fossil fuels of a finding that allegedly shows the higher the market penetration of renewables, the higher electricity prices. I demonstrated in the previous post that this is a spurious relationship and a more plausible reason for the empirical relationship is that market penetration is highly correlated with how rich (and expensive) a country is. Indeed, I showed that controlling for cost-of-living in a particular country, the relationship between market penetration of renewables and cost of electricity was not statistically significant.

I noted at the end of that post that I would show the results of a simple multiple linear regression of the before-tax price of electricity and market penetration of renewables across these countries.

But, first here is a chart of the results of the predicted price of before-tax electricity in a country given the cost-of-living, holding the market penetration of renewables constant. We see a strong positive relationship—the higher the cost-of-living in a country, the more expensive the before-tax cost of electricity.