Consider the following regression estimates (FNB) Linear regression Robust income Coef. Std. Err. hours _cons 18.91906 1.481248 281.4618 34.36264 where income is weekly income in NZS and hours is working hours per week. Number of obs F(1, 498) Prob > F R-squared Root MSE t P>|t| 12.77 0.000 8.19 0.000 500 163.13 = 0.0000 = 0.2880 = 593.03 [95% Conf. Interval] 16.0088 21.82933 213.9482 348.9754
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- A researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π: Bt = a0 + a1NIt + a2Π t + ut Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π. Using a sample of 56 annual observations, s/he estimates the following equations: (1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6 (3.58) (8.80) (-1.05) (2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9 (9.70) (16.7) (3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9 (8.84) (36.1) (4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…Consider the following multiple regression results for estimation of demand for coffee: Dc= 6.27+0.48DI-1.23Pc-3.5Pt+0.19Pm+0.07Ae. Where, Dc=Demand for coffee (in ‘000 dollars) DI=Disposable income Pc=Price index of coffee Pt=Price index of tea Pm=Price index of milk Ae=Advertising expenditure (in ‘000 dollars) Adjusted R square=0.90 Comment on the results including signs and coefficients of the multiple regression..Identify the assumption(s) of linear regression that is (are) violated in each of the following residual plots.
- The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The yearly income of a 24-year-old female individual is _____.The following measurements correspond to air velocity and the evaporation coefficient of burned fuel droplets in a boost engine. regression equation isy =0.0692+0.0038X A) Suppose that the linear relationship continues beyond the range of experimentation and finds the 95% prediction limits for an observation of the evaporation coefficient when the air velocity is 450 cm / s.Consider a linear regression model for the decrease in blood pressure (mmHg) over a four-week period with muy=2.8+0.8x and standard deviation chi=3.2. The explanatory variable x is the number of servings fruits and vegetables in a calorie-controlled diet. Using the 68-95-99.7 rule, between what two values would approximately 95% of the observed responses, y, fall when x = 7?
- Consider the following hypothetical regression, with FAIL? as a dummy variable for if a business failed in its first year (1=failed, 0=didn’t fail); LOAN is how much money, in thousands of dollars, the business got as a loan when it started; GIG? is a dummy variable for if there was a gig economy job available, such as driving for Lyft (1=available, 0=not available), and COMP is the number of existing competitors the business faced when it started. All variables are statistically significant. FAIL? = 0.63 – 0.01*LOAN – 0.08*GIG? + 0.05*COMP Answer the following: Determine the predicted value of FAIL? if the business had a $30,000 loan, there was no gig economy, and four competitors. In everyday language, what does the estimated value found in A mean? If a business gets an additional six thousand dollars in loans, how would FAIL? change? Give the “punchline” interpretation of the COMP variable: “For every additional competitor…”A surgery intern has conducted a study of the sleeping habits of her colleagues and has developed a following regression equation: y-hat = 6 + 0.1X, where X is the number of hours working on one shift, and Y is the number of hours sleeping at night after that shift. Yvette worked 10 hours and slept 8 hours. What is Yvette’s residual? 0.1 1 6 7The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.
- The following table shows the annual expenditures, in dollars, per customer unit for residential landline phone services and cellular phone services in the United States in the given year.† Year Landline Cell 2004 592 378 2006 542 524 2008 467 643 2010 401 760 Calculate the regression line for each type of service. (Let t be the time in years since 2004, L be the operating revenue of landline phone services and C be the expenditure of cellular services. Round your regression parameters to two decimal places.) L(t) = C(t) = Determine the expenditure level at which the two lines cross. Round your answer for the expenditure level to one decimal place. million dollarsThe following regression model describes the relation between the number of days of experience in a job involving the wiring of electronic components and the number of components which were rejected stack N u m b e r space o f space r e j e c t s with hat on top equals 249 minus 1.4 space D a y s space o f space e x p e r i e n c e Based on this model, estimate the number of components rejected for an employee with 97 days of experience in the job. Round your answer to one decimal place.The following estimated regression model was developed relating yearly income (y in $1000s) of 30 individuals with their age (x1) and their gender (x2) (0 if male and 1 if female).ŷ = 30 + 0.7x1 + 3x2Also provided are SST = 1200 and SSE = 384.The multiple coefficient of determination is _____.