In a study it was shown that for a sample of 353 college faculty, the correlation was 0.11 between annual raises and teaching evaluations. What would be the coefficient of determination of a regression of annual raises on teaching evaluations for this sample? Interpret your result.
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In a study it was shown that for a sample of 353 college faculty, the correlation was 0.11 between annual raises and teaching evaluations. What would be the coefficient of determination of a regression of annual raises on teaching evaluations for this sample? Interpret your result.
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- The following regression was run using a sample of 587 women living in Kenya. The variable goats is the number of goats the woman owns and grant is whether the woman received $ 500 in cash (in local currency equivalent) two years ago from the charity GiveDirectly, or not. The charity gives grants randomly to poor people in Kenya, of $ 500. goats = 6.42 +0.80 grant R2=0.35 1. What is the estimated coefficient for grant? What does it mean, in words? (Be specific, referring to numbers.) 2. Suppose one woman in the sample, Wangari, did not receive a grant. What is her predicted number of goats? Please do fast ASAP fastSuppose you examined blood of 36 patients with the aim to study the relation between sugar level in blood (in mg/dL) and the amount of artificial sweetener (measured in grams). Your regression shows: blood=7.1 + 0.4*sweatener - 0.2*female. a)What is the most precide interpretation of the estimated coefficient for sweetener? b)What is the most precide interpretation of the estimated coefficient for the constant?A guidance counselor wants to determine if there is a relationship between a student's number of absences, x, and their grade point average (GPA), y. The data that were collected are displayed in the scatterplot and the least-squares regression line was calculated. One student with 2 absences has a GPA of 1.8. This point is circled on the graph. GPA and Absences 4.8 4.4 4.0 3.6 3.2 2.8 2.4 2.0 1.6 4 6 8 10 12 14 16 Absences (Days) What effect does the circled point have on the standard deviation of the residuals? This point will increase the value of the standard deviation of the residuals because it has a large positive residual. This point will increase the value of the standard deviation of the residuals because it has a large negative residual. This point will not affect the value of the standard deviation of the residuals because it has a large positive residual. This point will decrease the value of the standard deviation of the residuals because it has a large negative residual.…
- A regression of average weekly earnings (AWE, measured in dollars) on age(measured in years) using a random sample of college-educated full-timeworkers aged 25–65 yields the following: AWE = 696.7 + 9.6 X Age, R2 = 0.023, SER = 624.1.a. Explain what the coefficient values 696.7 and 9.6 mean.b. The standard error of the regression (SER) is 624.1. What are the unitsof measurement for the SER? (Dollars? Years? Or is SER unit-free?)c. The regression R2 is 0.023. What are the units of measurement for theR2? (Dollars? Years? Or is R2 unit-free?)d. What does the regression predict will be the earnings for a 25-year-oldworker? For a 45-year-old worker?e. Will the regression give reliable predictions for a 99-year-old worker?Why or why not?f. Given what you know about the distribution of earnings, do youthink it is plausible that the distribution of errors in the regressionis normal? (Hint: Do you think that the distribution is symmetric orskewed? What is the smallest value of earnings,…What do you mean by the Sampling Distribution of the OLS Estimators in Multiple Regression?An economist believes that price, x, (in dollars) is the biggest factor affecting quantity sold, y. To support his argument, he collected data on price and quantity sold from a sample of 29 stores, selling the same product, and generated the regression output in Excel. The regression equation is reported as y = and the correlation coefficient r = - 0.333. 9.45x + 20.86 What proportion of the variation in quantity sold y can be explained by the variation in price? R² = % Report answer as a percentage accurate to one decimal place.
- Suppose you examined blood of 36 patients with the aim to study the relation between sugar level in blood (in mg/dL) and the amount of artificial sweetener (measured in grams). Your regression shows: blood=7.1 + 0.4*sweatener - 0.2*female. What is the most precide interpretation of the estimated coefficient for sweetener?INSUR A life insurance company wishes to examine the relationship between the amount of life insurance held by a family and family income. From a random sample of households, the company collected the accompanying data. The data are in units of thousands of dollars. INCOME 97 38 141 29 y = x = Let INSUR 280 75 INCOME 303 81 453 137 The numerator of the slope coefficient formula for the estimated regression equation is: 357 77 a 400,201.10 199 43 b 392,354.02 251 53 384,660.80 807 184 d 377,118.44 147 45 272 70 537 128 527 117 245 55 483 116 673 204 194 46 154 51 163 48 280 69 507 140 464 136 321 71 873 206 476 144 574 111 251 65 497 130 826 171 133 32 259 82 281 73 446 146 332 77 219 48 208 55 180 48 169 42 273 69 502 127 547 126 281 80 428 143 370 77 221 49 214 5197 90 90 87 2. Listed below are number of registered pleasure boats in Florida (tens of thousands) and the numbers of manatee fatalities from encounters with boats in Florida for each of several recent years. Pleasure boats Manatee fatalities a. Is there sufficient evidence to conclude that there is a linear correlation between numbers of registered pleasure boats and number of manatee boat fatalities? Assume requirement satisfied. Use a = 0.05 95 97 90 68 90 88 81 99 92 b. Find the regression equation. 99 73 83 90 73 c. In a year not included in the data, there were 970,000 registered pleasure boats in Florida, find the best predicted number of manatee fatalities resulting from encounters with boats.
- Mita, the manufacturer of copiers, has been spending increasing amounts of money on radio and television advertising in recent years. An analyst employed by Mita wanted to estimate a simple linear regression of the company's annual copier sales versus advertising dollars. Th regression results included SSE = 12593 and SSR = 87663. What is the coefficient of determination for this regression? 0.874 0.935 0.144 0.126Using a sample from a population of adults, to estimate the effects of education on health, we run the following regression: hypertension, = a + Beduc; + YX¡ + Ei where hypertension is a dummy variable equals one if a person suffers from hypertension and zero otherwise, educ is years of schooling, and X is a vector of demographic variables such as age, gender, and ethnicity. (a) Show that educ in the regression above is likely to be endogenous and discuss the consequences of this on the OLS estimators. (b) Evaluate whether a government policy that requires children to complete twelve years of schooling is a good instrumental variable for educ.A finance manager employed by an automobile dealership believes that the number of cars sold in his local market can be predicted by the interest rate charged for a loan. Interest Rate (%) Number of Cars Sold (100s) 3 5 10 7 8 2 The finance manager performed a regression analysis of the number of cars sold and interest rates using the sample of data above. Shown below is a portion of the regression output. Regression Statistics Multiple R0.998868 R2 0.997738 Coefficient |14.88462 Interest Rate -1.61538 Intercept 1. Are there factors other than interest rate charged for a loan that the finance manager should consider in predicting future car sales? 2. Is interest rate charged for a loan the most important factor to be considered in predicting future car sales? Explain your reasoning.The dealership's vice- president of marketing has requested a sales forecast at the prevailing interest rate of 7%. 3. As finance manager, what reasons would you convey to the vice-president in recommending…