The regression assumption is that the deviations from the regression line (residuals) follow a:
normal distribution
In regression analysis, one of the key assumptions is that the deviations from the regression line, known as residuals, are normally distributed. This assumption is critical because it underlies the statistical tests used to determine the significance of the predictors in the model.
The rationale behind this assumption is rooted in the Central Limit Theorem, which suggests that, under certain conditions, the sum of many independent random variables tends to follow a normal distribution regardless of the original distribution of the variables.
In practice, when assessing the validity of this assumption, analysts often use graphical tools like Q-Q plots or statistical tests such as the Shapiro-Wilk test to evaluate if the residuals appear to be normally distributed.
Hence, the correct answer to the question about the distribution that the residuals follow is:
normal distribution
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\(\begin{array}{ll} \mathrm{S}_{\mathrm{t}}=\alpha \mathrm{Y}_{\mathrm{t}} & 0<\alpha<1 \\ \mathrm{I}_{\mathrm{t}}=\beta\left[\mathrm{Y}_{\mathrm{t}}-\mathrm{Y}_{\mathrm{t}-1}\right] & \beta>0 \\ \mathrm{~S}_{\mathrm{t}}=\mathrm{I}_{\mathrm{t}} & \end{array}\)
where S t = Savings, Y t = Income, l t = Investment, t = time
In this model for economic growth, the condition for economic growth is
