2. (6 points) There is a hypothesis that males on average tend to perform better
ID: 3248850 • Letter: 2
Question
2. (6 points) There is a hypothesis that males on average tend to perform better at quantitative and spatial tasks, and females tend to perform better at verbal fuency and memory tasks. The data include four intelligence test scores (arithmetic reasoning, word knowledge, paragraph comprehension, and mathematical knowledge for random samples of 1,306 American men and 1,278 American women between the ages of 16 and 24 in 1981. To explore the data, we run a principal components analysis and a further analysis by regressing the second principal component to the gender of subjects Importance of components PC1 PC2 PC3. PC4 Standard deviation 1.7693 0.6823 0.47425 0.42320 Proportion of Variance 0.7826 0.1164 0.05623 0.04477 Cumulative Proportion 0.7826 0.8990 0.95523 1.00000 Rotation PC4 PC1 PC2 PC3 Arith -0.5083160 0.4512007 -0.00400 4488 -0.73349 6289 Word -0.5004186 -0.4454845 -0.738395683 0.076789450 Parag -0.4908641 -0.5583246 0.668788546 -0.006926482 Math -0.5002485 0.5350095 0.086473462 0.675306299 lm formula fit$xC, 21 Gender, data ex0222) Coefficients: Estimate Std. Error t value Pr (>lt (Intercept) -0.14881 0.01864. 7.984 2. 11e-15 0.29444 0.02622 11.230 2e-16 Gender male (a) (3 points) How many principal components do you want to keep for further analysis Justify your answer. What do those components stand for in terms of the test scores?Explanation / Answer
Part-a
We would keep first two components as these explained together 89.90% of the variability and thereafter there is marginal increase in variability.
These principal components are independent linear combination of original variables and represent overall intelligent test scores.
Part-b
From the regression analysis we observe that the coefficient of male is significant with p<0.05 and so male is significant predictor of intelligence test score and as its coefficient is positive so males have on an average 0.29444 higher intelligence test score as compared to females which is contrary to belief that females perform better
Part-c
The drawback I s that we should use first principal component as it explained most of the variability than other 3 componentns.
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