In the following time series linear regression equation, t is time in years and y issales in millions of dollars:ýt =Interpret the regression coefficient.= 11. 602 + 3.46tFor every one year increase in time, sales increase by $3.46 million on average.For every one year increase in time, sales decrease by $3.46 million on average.As time increases, sales fluctuate around a constant mean of $3.46 million.For every one year increase in time, sales decrease by $346 million on average.

Given time series linear regression equation, yt^=11.602+3.46t where 't' is time in years and 'y'…

Answered: In the following time series linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
While collecting data on shoe sizes (y) compared to heights in inches (x) of male students in the class a student found that the shoe sizes ranged from size 7 to size 11 and the heights of the students ranged from 60 to 72 inches. The student ran a linear regression to get the function = 1 -x- 3 13 where y is the shoe size and is the height of the person in inches. What would be the shoe size for a student who was 73 inches tall? Shoe sizes only show up in incriments of 0.5 (ie. 7, 7.5, 8, 8.5, 9, 9.5, ....) so round to the nearest 1/2 shoe size. Show all your work.
Data 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.
Develop a scatterplot and explore the correlation between customer age and net sales by each type of customer (regular/promotion). Use the horizontal axis for the customer age to graph. Find the linear regression line that models the data by each type of customer. Round the rate of changes (slopes) to two decimal places and interpret them in terms of the relation between the change in age and the change in net sales. What can you conclude? Hint: Rate of Change = Vertical Change / Horizontal Change = Change in y / Change in x
Bankers at a large financial institution created the linear regression model d = 0.37 – 0.0004s to predict the proportion of customers who would default on their loans, d, based on the customer's credit score, s. For a customer with a credit score of 700, which of the following is true? A The default proportion is predicted to be 0.09. В The default proportion will be 0.09. The default proportion is predicted to be approximately 1.75 million. The default proportion will be approximately 1.75 million. E The default proportion is predicted to be 0.28.
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?
M3
Use Excel to Run the Regressions:1. Wage and Age: Do you think a worker’s wage is related to his/her age? It is expected that wagesincrease with age up to certain age, after that wages go down. The “Wage Quadratic Data” fileposted contains data on the hourly wage (in $) for construction workers, workers’ ageand whether the worker has a bachelor’s degree or not (Graduate equals 1 if the worker has abachelor’s degree and 0 otherwise). Use the data file to answer the following questions:A) Build a model to predict the hourly wage of construction workers based on their education andage.B) Use the model to predict the hourly wage for a college graduate construction worker if his/herage is 30, 50, and 70c) Based on your model, calculate the age at which the hourly wage for construction workers ismaximized.
In linear regression analysis, the coefficient for the x-variable when the y-variable is regressed on the x-variable can be thought of as: Note: more than one answer may be correct Group of answer choices How much the value of the predicted y-variable will change when the x-variable changes by one unit. In the simple (two variable) linear regression model, the coefficient can be thought as the slope coefficient that measures the responsiveness of y to changes in x. The estimated coefficient will change if the sample containing x and y changes. The sample coefficient is an estimate of the population coefficient Before interpreting the coefficient for the x-variable, we should test whether the coefficient is statistically significant.
Let σ be the surface denoted by z = x² + y² + 2xy bounded by x² + y² = 2. Knowing that the density of a material that has the shape of σ is given by [image], determine the mass of this surface.
There is a linear relationship between the number of chirps made by the stiped ground cricket and the air temperature. It was determined that the linear regression model is: y = 25.2 + 3.3x where x is the number of chirps per minute and y is the estimated temperature in degrees Fahrenheit. What is the temperature if a cricket chirps 18 times? Round to the nearest degree. Di not include units.
A regression was run to determine if there is a relationship between hours of TV watched per day (xx) and number of situps a person can do (yy).The results of the regression were:y=ax+b a=-0.629 b=39.045 r2=0.806404 r=-0.898 Use this to predict the number of situps a person who watches 6.5 hour(s) of TV can do, and please round your answer to a whole number.

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