1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn- ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported t-statistic for the slope coefficient is 3.95. (a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of education is equal to 8% against the alternative that the rate of return to education is more than 8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion, with its economic interpretation. [Hint: From the information you should be able to figure out the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you should be able to find the t statistic.] (b) Construct a 95% interval estimate for the return to an additional year of education and state its interpretation.

1. Using data from 2013 on 64 black females, the estimated log-linear regression between WAGE (earn- ings per hour, in $) and years of education, EDUC is ln(WAGE) = 1.58+0.09EDUC. The reported t-statistic for the slope coefficient is 3.95. (a) Test at the 5% level of significance, the null hypothesis that the return to an additional year of education is equal to 8% against the alternative that the rate of return to education is more than 8%. In your answer, show (i) the formal null and alternative hypotheses, (ii) the test statistic and its distribution under the null hypothesis, (iii) the critical value from the t table and the rejection region (in a figure), (iv) the calculated value of the test statistic, and (v) state your conclusion, with its economic interpretation. [Hint: From the information you should be able to figure out the standard error of the slope coefficient (se(b₂)). Then, with the calculated standard error, you should be able to find the t statistic.] (b) Construct a 95% interval estimate for the return to an additional year of education and state its interpretation.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age in years (X1) and their gender (X2) (0 if male and 1 if female). The yearly income of a 24-year-old female individual is
Consider a hypothetical regression predicting if someone will be married or not by the age of 40, MARRIED? (1 means this person is married by the age of 40 and 0 means this person is not married by the age of 40). The regression is as follows (all variables are statistically significant): MARRIED? = 0.2 + 0.03*EDUCATION - 0.01*BMI Where EDUCATION is the number of years of education someone's had and BMI is their body mass index. Suppose someone had 20 years of education and a BMI of 25. What is the predicted value of MARRIAGE? 0.35, which makes sense even though MARRIED? can only be a zero or one 0, because the calculated value is 0.35 so we round down. 0.55, which makes sense even though MARRIED? can only be a zero or one. Calculating a predicted value should not be done here because the dependent variable is a dummy variable. 1, because the calculated value is 0.55 so we round up.
Consider a hypothetical regression predicting if someone will be married or not by the age of 40, MARRIED? (1 means this person is married by the age of 40 and 0 means this person is not married by the age of 40). The regression is as follows (all variables are statistically significant): MARRIED? = 0.2 + 0.03*EDUCATION - 0.01*BMI Where EDUCATION is the number of years of education someone's had and BMI is their body mass index. Suppose someone had 20 years of education and a BMI of 25. What is the predicted value of MARRIAGE? a 0, because the calculated value is 0.35 so we round down. b 0.55, which makes sense even though MARRIED? can only be a zero or one. c 0.35, which makes sense even though MARRIED? can only be a zero or one d Calculating a predicted value should not be done here because the dependent variable is a dummy variable. e 1, because the calculated value is 0.55 so we round up.
Consider a hypothetical regression predicting if someone will be married or not by the age of 40, MARRIED? (1 means this person is married by the age of 40 and 0 means this person is not married by the age of 40). The regression is as follows (all variables are statistically significant): MARRIED? = 0.2 + 0.03*EDUCATION - 0.01*BMI Where EDUCATION is the number of years of education someone's had and BMI is their body mass index. Suppose someone had 20 years of education and a BMI of 25. Complete this sentence: For every additional year of education someone has:... a ...their chance of getting married by 40 increases by 0.03 percentage points. b ...their chance of getting married by 40 increases by 3 percentage points. c ...their chance of getting married by 40 increases by 0.03. d ...their chance of getting married by 40 increases by 3%. e This regression means nothing because the dependent variable is a dummy variable.
An investigation into the relationship between an adolescent mother's age x in years and the birth weight y of her baby in grams yielded the regression equation y= - 1163.45 + 245.15x as well as r = .88369, r2= .78091, SSE = 337212.45, and s= 205.30844 1) What is the predicted birth weight for a baby brn to a 17 year old woman? 2) What is the propotion of the variability in the weights of babies born to adolescent mothers that is accounted for by the mother's age? 3) For every additional year in the mother's age that mean birth weight of the baby? (a) increases by about 245g (b) decreases by about 245g (c) increases by about 1163g (d) increases by about 1163g (e) changes by an amount that cannot be determined from the information given.
In a study of possible correlation between the height in cm (X) and the weight in kg (Y) of chimpanzees, a sample of 40 animals produces a correlation coefficient of r=0.813 and a regression line with equation Y=0.34X+19.5. What is the expected weight of a chimpanzee that is 157 cm tall? Round off final answer to 2 decimal places.
If we collect monthly sales over two years for N=100 stores, we should not apply a simple linear regression model directly to the data, because the observations are not independent with each other. Is this statement True or False? A) True B) False
Assume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment?