We have the test scores, happiness index, fertility rates, urbanization rates, and GDP of the following countries: Albania, Argentina, Australia, and Austria.

- Albania:
- Test score = 405
- Happiness index = 4.586
- Fertility = 1.64
- Urbanization rate = 62.1
- GDP = 13,496

- Argentina:
- Test score = 402
- Happiness index = 6.388
- Fertility = 2.4
- Urbanization rate = 92.1
- GDP = 23,291

- Australia:
- Test score = 503
- Happiness index = 7.272
- Fertility = 1.95
- Urbanization rate = 86.2
- GDP = 50,193

- Austria:
- Test score = 484
- Happiness index = 7.139
- Fertility = 1.4
- Urbanization rate = 58.7
- GDP = 56,960

Questions:

i. Use R-Studio to run a simple regression of PISA scores on the happiness index. Import all this data into your R-Studio without listing the variables individually. Show all the code used to run the regression and all the results of the regression.

ii. Based on your results, does happiness have a positive effect on test scores? Why or why not?

iii. Is the causal effect of interest statistically significantly different from zero at the 5% significance level? Why or why not?

To run a regression of PISA scores on happiness index using R-Studio, import the data, define the regression model, and view the results using the 'lm' and 'summary' functions. The coefficient of the happiness index variable will determine if happiness has a positive effect on test scores. The p-value associated with the coefficient will determine if the effect is statistically significant.

Explanation:

To run a simple regression of PISA scores on happiness index using R-Studio, you can start by importing the data into R-Studio. Then, you can use the 'lm' function to define the regression model. Finally, you can use the 'summary' function to view the results of the regression which will include coefficients, p-values, and other relevant statistics.

Import the data:
data <- read.csv('data.csv')
Run the regression:
regression_model <- lm(Test_score ~ Happiness_index, data = data)
View the results:
summary(regression_model)

Based on the results of the regression, you can determine if happiness has a positive effect on test scores by examining the coefficient of the happiness index variable. If the coefficient is positive and statistically significant, it indicates a positive effect of happiness on test scores.

To determine if the causal effect of interest is statistically significantly different from zero at the 5% significance level, you can look at the p-value associated with the coefficient of the happiness index variable. If the p-value is less than 0.05, you can conclude that there is a statistically significant effect of happiness on test scores.

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