Please answer all parts to the question and explain any math used. I am having t
ID: 3275517 • Letter: P
Question
Please answer all parts to the question and explain any math used. I am having trouble with breaking down the parts of the equation and understanding where some of the information is coming from within the equation. Thanks!
(b) It is important to see if IQ score has a significant effect on wages. State the null and the alternative hypothesis, and evaluate if IQ score helps to explain the log of wages at 1 and 5 percent of significance level.
(c) What is your conclusion about the relation between wages and IQ. Feel free to critize the model.
reg lwage ig df MS 935 102.62 0.0000 0.0991 0.0981 39995 Source Number oi ob8- F (1, 933) Model Residual 16.4150981 149.241196 1 16.4150981 Prob> F 933 15995841 R-squared Adj R-squared = Total 165.656294 934.177362199 Root MSE 1wage Coef. Std. Err. [95% Conf. Interval] 007101 5.71229 0088072 .0008694 .0890206 iq 10.13 0.000 .0105134 cons 5.886994 66.13 0.000 6·061698 predict yhat option xb assumed; fitted values) scatter logwage iq | line yhat iqExplanation / Answer
a) Describe briefly the economic and statistical meaning of the model. In particular, we are interested in the estimate of the effect of IQ scores on ages. Based in the sample, report the sign and magnitude of the ‘IQ effect’ on wages. Is this effect economically relevant? What is the predicted increase in wages if worker’s IQ increases in 10 points?
Answer:
The given regression model explains the relationship between the two variables such as IQ scores and wages. For this regression model, researcher used the dependent or response variable as wages and independent variable or predictor as IQ scores. For the given regression model for estimation of the wages, the regression equation is given as below:
Wages = 0.0088072 + 5.886994*IQ
For this regression equation, y-intercept is given as 0.0088072 and slope is given as 5.886994. The positive slope indicates the positive linear relationship exists between the two variables wages and IQ scores. The value of R squared or coefficient of determination is given as 0.0991. This indicate the correlation coefficient would be sqrt(0.0991) = 0.314802. This means there is a considerable positive linear association exists between the given two variables. Yes, this effect is economically relevant as we know that high IQ scores of workers would be responsible for extra percent salary increase.
Now, we have to predict the increase in wages if worker’s IQ increase in 10 points.
Wages = 0.0088072 + 5.886994*10
Wages =58.87875
Predicted increase in wages would be 58.88% as there is 10 points increase in IQ scores.
(b) It is important to see if IQ score has a significant effect on wages. State the null and the alternative hypothesis, and evaluate if IQ score helps to explain the log of wages at 1 and 5 percent of significance level.
Answer:
Here, we have to check whether the IQ score has statistically significant effect on wages or not. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The IQ scores have no any statistically significant effect on wages.
Alternative hypothesis: Ha: The IQ scores have statistically significant effect on wages.
For checking the above claim or hypothesis, we use F test and we get the following results:
Test statistic = F = 102.62
P-value = 0.00
Alpha values = 1% and 5% ( = 0.01 and 0.05)
For both alpha values, the P-value is less. So, we reject the null hypothesis that IQ scores have no any statistically significant effect on wages.
There is sufficient evidence to conclude that IQ scores have statistically significant effect on wages.
(c) What is your conclusion about the relation between wages and IQ. Feel free to critize the model.
Answer:
From the above analysis, it is found that there is a considerable positive linear association or relationship exists between the two variables wages and IQ scores. The relationship found to be statistically significant and that’s why we can use this model for the estimation purpose. Although model is statistically significant, but due to low correlation coefficient or coefficient of determination, we cannot use this model for entire population. Coefficient of determination is given as 0.0991 which means only 9.91% of the variation in the dependent variable wages is explained by the independent variable IQ scores.
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