Hourly Wage Linear Regression
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Data from a study of 534 U.S. workers from 1985 includes information about each worker's hourly wage (measured in U.S. dollars/hour) and age (measured in years). First, linear regression is performed to estimate the relationship between hourly wage and age (years), and the resulting slope of age is 0.08, and correlation coefficient (r) = 0.18. (both are positive) This analysis is repeated with the same data, but the units of age are changed from years to months (age in years / 12), and a second regression is performed relating hourly wages to age (months). In this repeated analysis (compared to the first):
a. the slope and correlation coefficient would both increase
b. the slope and correlation coefficient would both decrease
c. the slope would increase, but the correlation coefficient would remain the same
d. the slope would decrease, but the but the correlation coefficient would remain the same
e the slope would remain the same, but the correlation coefficient would increase
f. the slope would remain the same, but the correlation coefficient would increase
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Solution Summary
The solution identifies the correct option of what the second regression analysis would be like compared to the first. Brief explanations with examples are included for further understanding.
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The answer is
d. the slope would decrease, but the but the correlation coefficient would remain the same
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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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