1. Consider the following table.

Call:lm(formula = y ~ x)Residuals: Min 1Q Median 3Q Max-15.0513 -4.2581 -0.3658 3.8598 15.9399Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -3.6019 1.0323 -3.489 0.000528 *** x 5.0418 0.1001 50.343 < 2e-16 ***---Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.'0.1 ' ' 1Residual standard error: 6.538 on 498 degrees of freedomMultiple R-squared: 0.8358,Adjusted R-squared: 0.8354F-statistic: 2534 on 1 and 498 DF, p-value: < 2.2e-16

1. Put the information in the above table into equation form.
2. What is the marginal effect of x?
3. Is the coefficient for x statistically significant?
4. What does statistical significance mean in this case?
5. How much of the variation in y is being explained by x?
6. What is the predicted value for x=10?
7. What is the residual for x=10 and a y=40?
8. Suppose that we have an equation y_i=1 + 2x_i+3z_i+2x_iz_i. Suppose that x and z are both continuous variables. For a z_i=5, which is the mean of z, what is the marginal effect of x?
9. Now suppose that z is a dummy variable. What is the marginal effect of x if the condition for the dummy variable is satisfied?
10. Note that sometimes the information about a regression will not come in the form of the table you see above. Sometimes I will simplify it for you as I do below (note that I omit the star system). Redo the questions in part 1 with the table below (except for the variation in the y variable).

Coefficients:
	Estimate	St. Error	t-value	Pr(>|t|)
Intercept	-17	1.82	0.26	0.0049
x	2.456	2.00	3.899	0.00657

For the table above, evaluate whether or not the relationship in the table directly above is substantively significant using the values in the following tables.

The distribution of x.

Min	1st Quartile	Median	3rd Quartile	Max
0	5	10	15	20

The distribution of y.

Min	1st Quartile	Median	3rd Quartile	Max
0	15	30	45	60