d. The linear model illustrated in diagram is GPA = a + ß*Hours-Studied + u. What does it mean that Hours-Studied are orthogonal to u? e. How is B estimated? f. Explain why an estimator of ß can only be accurate (unbiased) when E(u₁|xi) = 0?

A county real estate appraiser wants to develop a statistical model to predict the appraised value of houses in a section of the county called East Meadow. One of the many variables thought to be an important predictor of appraised value is the number of rooms in the house. Consequently, the appraiser decided to fit the simple linear regression model, y = b₁x + bowhere y = appraised value of the house (in $thousands) and x = number of rooms. Using data collected for a sample of n=74 houses in East Meadow, the following results were obtained: y=74.80+ 17.80x Give a practical interpretation of the estimate of the slope of the least squares line. For each additional room in the house, we estimate the appraised value to increase $74,800. 1000 For each additional dollar of appraised value, we estimate the number of rooms in the house to increase by 17.80 rooms. For a house with 0 rooms, we estimate the appraised value to be $74,800. For each additional room in the house, we estimate the…

A simple linear regression that describes the effect of individuals’ cigarette smoking on health is given by Health = α + β * cigarettes + u, where Health is a measure of health that is on the scale of 1 to 5, where 1 means excellent health and 5 means poor health. So the bigger the number, the worse the health. cigarettes is the average number of cigarettes smoked per day; the unobservable u is an individual’s health consciousness. Note that health conscious person tends to live a healthy life in general.   What will happen to β if cigarettes is in terms of weekly rather than daily?

A 1 Demand 2 WN 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 7.38 8.51 9.52 7.50 9.33 8.28 8.75 7.87 7.10 8.00 7.89 8.15 9.10 8.86 8.90 8.87 9.26 9.00 8.75 7.95 7.65 7.27 8.00 8.50 8.75 9.21 8.27 7.67 7.93 9.26 B PriceDif -0.05 0.25 0.60 0.00 0.25 0.20 0.15 0.05 -0.15 0.15 0.20 0.10 0.40 0.45 0.35 0.30 0.50 0.50 0.40 -0.05 -0.05 -0.10 0.20 0.10 0.50 0.60 -0.05 0.00 0.05 0.55 C

Let y = sales at a fast-food outlet (1000s of $), x, = number of competing outlets within a 1-mile radius, x, = population within a 1-mile radius (1000s of people), and x, be an indicator variable that equals 1 if the outlet has a drive-up window and o otherwise. Suppose that the true regression model is Y = 12.00 - 1.1x, + 6.8x, + 15.3x, + E (a) What is the mean value of sales when the number of competing outlets is 3, there are 8000 people within a 1-mile radius, and the outlet has a drive-up window? (Round your answer to one decimal place.) thousand dollars (b) What is the mean value of sales for an outlet without a drive-up window that has four competing outlets and 4000 people within a 1-mile radius? (Round your answer to one decimal place.) thousand dollars (c) Interpret B. O There are on average 15.3 fast-food outlets with drive-ups in a 1 mile radius. O It takes $15,300 to build a drive-up. O Approximately 1 in 15.3 fast-food outlets have drive-ups. O A drive-up will add…

Suppose that you believe that a quadratic relationship exists between the independent variable (of time) and the dependent variable Ý. Which of the following would represent a valid linear regression model? Y = bo + b1 X, where X = time4 Y = bo + b1 x4, where X = time Y = bo + b1 x2, where X = time Y = bo + b1 X, where X = time?

3. Given the following regression: Wage = 10 + 1.2 x male + 2 x educ + 0.15 x (male x educ) + u The dependent variable is hourly wage. There are three independent variables: a binary variable indicating male, years of education, and an interaction between male and educ. (a) Plot the relationship between wage and education for males and females separately. Put wage on the vertical axis and education on the horizontal axis. (hint: see Panel (b) of Figure 8.8 in the textbook; You may draw the graph on software or on a piece of paper and paste the snapshot below.) (b) According to the regression function above, (1) which gender has a higher base wage (for people with no education)? (2) which gender has higher return to education? (3) what's effect of an additional year of education on wage for females? (4) what's the effect of an additional year of education on wage for males? On * Accessibility: Investigate

We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.

Suppose there is 1 dependent variable (dissolved oxygen, Y) and 3 independent variables (water temp X1, depth X2, and hardness of water X3). Below is the result of the multiple linear regression.Which of the following is the equation of the multiple regression model?    Y = 4.36 + 0.37X1 + 0.24X2 + 0.04X3       Y = 0.00 + 0.02X1 + 0.56X2 + 0.37X3       Y = 24.84 - 1.17X1 - 0.15X2 - 0.04X3       Y = 5.69 – 3.20X1 - 0.61X2 -0.95X3

An industrial psychologist examined the number of absences for employees in Company A. She wanted to look into a possibility that the number of absences may regressed onto the level of stress that employees feel. The following data set below indicates perceived level of stress (Variable X) for a sample of 10 employees in Company A and the number of their absences in one month (Variable Y). A greater number for X indicates a higher level of stress. If you find a linear regression equation, what is the regression slope from the data below? Enter the number using decimal points (use two decimal points). Round to the closest second decimal point. For instance, if your answer is 0.3456, enter "0.35" Level of Stress (X) 2 1 3 7 2 5 2 4 8 6 # of Absences (Y) 4 7 6 9 6 8 7 10 11 7