Assume that you have a sample of 20 observations for the random variables X and Y and wish to estimate the population regression function $Y_i = \beta_0 + \beta_1 X_i + u_i$, using OLS. Suppose you calculate the following sums: $\sum(Y_i - \bar{Y})(X_i - \bar{X}) = 55$, $\sum(X_i - \bar{X})^2 = 62$, $\bar{Y} = 4.5$ and $\bar{X} = 5.5$ Based on the above, what are the values for $\beta_0$ and $\beta_1$, respectively? a) 1.83 and 0.67 b) -0.8871 and -0.3790 c) -0.3790 and 1.8871 d) -0.3790 and 0.8871 e) none of the above
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The sample mean of X is given by: \(\bar{X} = \frac{\sum X}{n}\) where \(\sum X\) is the sum of all the X values and n is the number of observations. In this case, \(\sum X = 55\) and n = 20, so: \(\bar{X} = \frac{55}{20} = 2.75\) The sample mean of Y is given Show more…
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