List of top Statistics for Economics Questions on Correlation and Regression

A regression equation 𝑌 = −2.5 + 2𝑋 is estimated using the following data:

𝑌	2	5	9	14
𝑋	2	4	6	8

The coefficient of determination is ________ (rounded off to two decimal places).

Let 𝑦̂=5.5+3.2 𝑥 be an estimated regression equation using a large sample. The 95% confidence interval of the coefficient of 𝑥 is [0.26, 6.14] and 𝑅² = 0.26. The standard error of the estimated coefficient is _______ (round off to 1 decimal place).

Suppose that the regression model is $Y_i =\beta_0 + \beta_1 X_{1i} + \beta_2 X_{2i} + \mu_i, i = 1, 2,..., n$. Which of the following null hypotheses could be tested using the F-test?