d-f please 1. Consider the simple linear regression modelY₁ = a + BX₁ + u₁, where i denotes an observation, Y and X is the outcome explanatory variablesand u is the error term.a. Suppose Y denotes GPA and X denotes study hours per week. Suppose that the relationshipbetween study hours and GPA is deterministic. Specifically, if you do not study your GPA forsure will be a miserable 0.3. And, for every hour you study, your GPA will for sure increaseby 0.25 points. Write the equation for this deterministic relationship. And, plot GPAconditional on study hours, where these hours runs from 0 to 16 on the X-axis. Why is uialways equal to 0?b. Why is this deterministic relationship a completely unrealistic view of reality?C.Illustrate on your figure random errors, u₁, that are positive shocks indicating that thedeterministic model underpredicts the GPA. And illustrate random errors that are negativeshocks indicating the model overpredicts.d. The linear model illustrated in diagram is GPA = a + ß* Hours-Studied + u. What does it meanthat Hours-Studied are orthogonal to u?e.How is 3 estimated?f. Explain why an estimator of ß can only be accurate (unbiased) when E(u₁|xi) = 0?

In this problem, we're dealing with a simple linear regression model where the outcome variable…

Answered: d. The linear model illustrated in…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 91E

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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?
In a linear regression model, the dependent variable is "Final exam score (%) for WPC 300" and the independent variable is "Hours studied". A coefficient of 4 could be interpreted as for every one % increase in the final exam score, the expected hours of study is 4. four hours of additional study, the expected increase in the final exam score is 1%. four hours of additional study, the final exam score is expected to increase by 4%. hour of additional study, the expected final exam score increases by 4%.
Consider the simple linear regression model Wage = Bo + B1*Age + U. The error term U can capture the followings, with the exception of O A. possible measurement error in Wage. O B. the temperature in London Ontario tomorrow. O C. possible model misspecification, such as the nonlinear effect of Age on Wage. O D. other variables that affect the dependent variable, such as previous work experience.
The term 'simple' in simple linear regression refers to the fact that a. the dependent variable is dichotomous b. there are multiple dependent and independent variables c. there is one independent variable d. there is more than one independent variable e. there are no independent variables
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 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
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?

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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?