Consider the following model: yhat = -0.7+-2.1x2 The prediction of y is yhat. What is the estimated marginal effect of x on y when x-0.17
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- Q5/ Use Linear Regression to fit the following data: 1 2 4 5 6. Y 4 9 10 10 8For a MR model with 4 predictors, we have: SSE 288 and SST = 957 What percentage of the variation in Y is accounted for by its assumed relationship with the predictors?A statistics professor wants to use the number of hours a student studies for a statistic final exam (x) to predict the final exam score (y). A regression model was fit based on data collected for a class during the previous semester, with the following results: y =35.0 + 3x Which of the following is the correct interpretation of the regression coefficient (slope)? Select the correct response: When the student does not study for the final exam, the mean final exam score is 35.0. None of the above are an interpretation of the slope For each increase of one hour in studying time, the mean change in the final exam score is predicted to be 35.0 For each increase of one hour in studying time, the mean change in the final exam score is predicted to be 3.0.
- The number of banks in a country has been dropping steadily since 1984, and the trend in recent years has been roughly linear. The annual data for the years 1999 through 2008 can be summarized as follows, where x represents the years since 1990 and y the number of banks, in thousands. n=10 Ex-235 ²-5605 Ey-77.564 Ey²=603.80424 Exy-1810.155 a. Find an equation for the least squares line. b. Use your result from part a to predict the number of banks in the year 2020. c. If this trend continues linearly, in what year will the number of banks drop below 6200? d. Find and interpret the correlation coefficient.Select the appropriate interpretation for the slope of the linear regression equation below. Y (Dependent Variable) = Grade Point Average X (Independent Variable) = Average number of hours spent using electronic devices for entertainment purposes yhat = 4 - 0.125*X A. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will increase on average by 0.125 points B. For every 1 GPA gained obtained by a student then on average that person will have watched 0.125 hours fewer of entertainment on electronic devices per week C. For every 1 GPA point lost by a student then on average that person will have watched 0.125 hours more of entertainment on electronic devices per week D. For every 1 hour more spent using electronic devices for entertainment per week then a person's GPA will decrease on average by 0.125 pointsData from 147 colleges from 1995 to 2005 (Lee,2008) were tested to predict the endowments (in billions) to a college from the average SAT score of students attending the college. The resulting regression equation was Y = -20.46 + 4.06 (X). This regression indicates that: a. for every one-point increase in SAT scores, a college can expect 4.06 billion more in endowments. b. most colleges have very high endowments. c. for every one-point increase in SAT scores, a college can expect 20.46 billion fewer in endowments. d. for every one-dollar increase in endowments, the college can expect a half-point increase in SAT scores.
- An engineer creates a model to predict the electric consumption of a household in summer in a day with a predictor variable of the number of hours the air-conditioner is running. The electric consumption is only at 26 kWh per day if aircon is not used. If the aircon was used by 1 hr, the electric consumption would increase by an additional 1.44 kWh. Find the average electric consumption if the aircon is used 15 hrs.For half-life demonstration, plot ln(half-lives) in the x-axis vs ln(no. of “tails-up” coins) in the y-axis. Perform linear regression to obtain the value of the slope, the value of the y-intercept, and the correlation coefficient r. What is the significance of these values?A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?
- A particular article used a multiple regression model to relate y = yield of hops to x₁ = mean temperature (°C) between date of coming into hop and date of picking and x₂ = mean percentage of sunshine during the same period. The model equation proposed is the following. y = 415.116.6x₁4.50x2+e (a) Suppose that this equation does indeed describe the true relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 39? (b) What is the mean yield when the mean temperature and percentage of sunshine are 19.1 and 42, respectively? You may need to use the appropriate table in Appendix A to answer this question.The following equation describes the relationship between output and labor input at a sample of work stations in a manufacturing plant ŷ = 2.35+2.20X. Suppose, for a selected workstation, the labor input is 5, the predicted output is?In calculating a simple regression for average number of drinks consumed (x) and grade point average (y), you get a slope coefficient (b) of -.15 and a y intercept of 2.50. Using the formula Y = a + bX, what would the predicted grade point average be for a student who averaged 1.0 drinks per week?