27 - It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown. The value of the measured t-test statistic to test whether mean SALARY depends linearly on HOURS is Regression Statistics Multiple R R Square Adjusted R Square 0.8857 0.7845 0.7801 Standard Error 1.3704 Observations 51 ANOVA df SS MS F Significance F Regression Residual 1 335.0472 335.0473 178.3859 1.8782 Total 50 427.0798 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Intercept Hours -1.8940 0.4018 -4.7134 0.0000 -2.7015 -1.0865 0.9795 0.0733 13.3561 0.0000 0.8321 1.1269 Note: 2.051E-05 = 2.051*10 and 5.944E – 18 =5.944*10-18

27 - It is believed that, the average numbers of hours spent studying per day (HOURS) during undergraduate education should have a positive linear relationship with the starting salary (SALARY, measured in thousands of dollars per month) after graduation. Given below is the Excel output for predicting starting salary (Y) using number of hours spent studying per day (X) for a sample of 51 students. NOTE: Only partial output is shown. The value of the measured t-test statistic to test whether mean SALARY depends linearly on HOURS is Regression Statistics Multiple R R Square Adjusted R Square 0.8857 0.7845 0.7801 Standard Error 1.3704 Observations 51 ANOVA df SS MS F Significance F Regression Residual 1 335.0472 335.0473 178.3859 1.8782 Total 50 427.0798 Standard Coefficients Error t Stat P-value Lower 95% Upper 95% Intercept Hours -1.8940 0.4018 -4.7134 0.0000 -2.7015 -1.0865 0.9795 0.0733 13.3561 0.0000 0.8321 1.1269 Note: 2.051E-05 = 2.05110 and 5.944E – 18 =5.94410-18

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?
suppose Zenos Manufacturing is contemplating investing in a new business. An existing company in the target industry has an equity beta of 0.90 but is very conservatively financed with a market value, equity-to-value ratio 95%. Zenos intends to use an equity-to-value ratio of 30%. What beta should Zeno use in estimating a cost of capital in the new business?
The relationship between sleep hours and overall happiness level on the next day was estimated as below in a linear format. (Happiness level is measured through a five-point scale: 1 = Extremely unhappy, 5 = Extremely happy) Overall happiness level = 0.27 * Sleep hours + 2.34 (The p-value for the coefficient of Sleep hours is 0.02.) Based on this equation, what is the expected happiness level of a person on a certain day, when he slept 7 hours the day before?
Airphone, Inc., manufactures cellular telephones at a pro-cessing cost of $47 per unit. The company produces an average of 250 phones per week and has a yield of 87%good-quality phones, resulting in 13% defective phones,all of which can be reworked. The cost of reworking adefective telephone is $16.a. Compute the quality-productivity ratio (QPR).b. Compute the QPR if the company increased theproduction rate to 320 phones per week while reducingthe processing cost to $42, reducing the rework cost to$12, and increasing the product yield of good-qualitytelephones to 94%.
7.1 What is a join hypothesis? What is the hypothesis that is being tested by constructing the overall regression F-statistic in the multiple regression model? 7.3 What is a control variable and how does it differ from the variable of interest? Do coefficients on control variables measure causal effect? 8.3 How is the slope coefficient interpreted in a log-linear model, where the dependent variable is in a logarithm form but the independent variable is not? In a linear-log model? In a log-log model? 9.1 Explain the difference between internal validity and external validity. Is it possible for an econometric study to have internal but not external validity? 9.3 What is the effect of measurement error in Y? How is it different from the effect of measurement error in X? 9.4 What is sample selection bias?
A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). (a) Calculate the expected profit if the firm follows this benchmark strategy, i.e., E(L)
A manufacturing firm, Caleb Corp, produces and sells product in its home (US) market, and in a foreign market. There is inherent risk in the revenues collected from the foreign market due to volatility in the exchange rate. Under a benchmark strategy, all of the production takes place in the home country. The resulting expected profits for Caleb Corp are variable, due to variation in the exchange rate. As an approximation, the firm has estimated profits for five possible ranges of the exchange rate, with profit represented as a lottery, L= (.2, 150; .2, 200; .3, 220; .2,250; .1, 270) The probabilities are estimated probabilities for the different ranges. The outcomes in this lottery are the estimated final profit levels (not changes in profit). Now suppose the firm can also buy forward contracts on foreign currency to neutralize the effect of the exchange rate on profits. Assume that these provide complete hedging, but that it involves an additional cost, so that following the…
24) If the R-square value for a simple linear regression model is 0.80 and the regression line has anegative slope, the correlation coefficient describing the relationship between the two variables is_____________.
Test the null hypothesis that the slope coefficient for ‘GROWTH’ is less than or equal to 0.07 against the alternative that it is greater than 0.07 (i.e. <=0.07 OR >0.07). The critical t value is 1.645 for a one-tailed test at the 5% significance level.
Weekly downtime of internet services from an internet service provider (in hours) has expected value 0.5 and variance 0.25. Based on past experience, the data scientist of a retailer store has calculated the loss function to the store from the downtime as C=30X+2X2 where X is the amount of weekly downtime and C is cost. Find the Expected cost, i.e, E(C).
A scientific foundation wanted to evaluate the relation between y= salary of researcher (in thousands of dollars), x1= number of years of experience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= an index of success in obtaining grant support. A sample of 35 randomly selected researchers was used to fit the multiple regression model. Parts of the computer output appear below. Based from the table, what is the constant term of the multiple linear regression?
The chief economist for Argus Corporation, a large appliance manufacturer, estimated the firm’s short-run cost function for vacuum cleaners using an average variable cost function of the form AVC = a + bQ + cQ2 where AVC = dollars per vacuum cleaner and Q = number of vacuum cleaners produced each month. Total fixed cost each month is $180,000. The following results were obtained: a) Are the estimates ˆa ,ˆb , and cˆ statistically significant at the 2 percent level of significance? Which is/are significant and which is/are not? b) Do the results indicate that the average variable cost curve is ∪-shaped? How do you know?c) If Argus Corporation produces 8,000 vacuum cleaners per month, what is the estimated average variable cost? Marginal cost? Total variable cost? Total cost? d) Answer part c, assuming that Argus produces 10,000 vacuum cleaners monthly. e) at what level of output will average variable cost be at a minimum? What is the minimum average variable cost?