You may need to use the appropriate technology to answer this question.Suppose data on advertising expenditures and revenue (both in thousands of dollars) for a certain restaurant follow.AdvertisingExpendituresRevenue1923344339105314532054(a) Let x equal advertising expenditures (in thousands of dollars) and y equal revenue (in thousands of dollars). Use the method of least squares to develop a stralght lineapproximation of the relationship between the two variables. (Round your numerical values to two decimal places.)

The regression equation is given by y' = a + bx

Answered: You may need to use the appropriate…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.
A chemical engineer discovered that by adding different amounts of an additive to gasoline, he could reduce the amount of nitrous oxides (NOx) from a car engine. A specified amount was added to one gallon of gasoline and the total amount of NOx in the exhaust was collected. Assume, in suitable units, that the data is: amount of additive 1 2 3 4 5 Nox 19 17 14 13 12 a) Obtain the least squares fit, of a straight line, for the amount of NOx b) Test whether or not the slope is β = 0. Consider a significance level of 0.01. c) Provide a 99% confidence interval for the mean value of NOx when the amount of additive is 9.
What is the least-squares line approximation to a set of datapoints? How is the line determined?
Draw a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Then draw the least-squares regression line on the graph.
Use the least squares regression to fit a straight line to: Along with the slope and intercept, compute the standard error of the estimate and the correlation coefficient. Plot the data and the regression line
Prove the result that the R^2 associated with a restricted least squares estimator is never larger than that associated with the unrestricted least squares estimator. Conclude that imposing restrictions never improves the fit of the regression.
Design a 3rd order Least-squares function approximation to interpolate between the mid between (2n and 3") for a dataset as chosen by you. Compute the LS model error.
A scientific foundation wanted to evaluate the relation between y= salary of researcher (in thousands of dollars), x1= number of years of experience, x2= an index of publication quality, x3=sex (M=1, F=0) and x4= an index of success in obtaining grant support. A sample of 35 randomly selected researchers was used to fit the multiple regression model. Parts of the computer output appear below. The least squares line fitted to the data is: salary = 2.001 + 0.33 x1 + 0.04 x2 + 0.69 x3 + 0.30 x4 + ε salary = 17.85 + 1.10 x1 + 0.32 x2 + 1.59 x3 + 1.29 x4 + ε salary = 2.001 + 0.33 x1 + 0.04 x2 + 0.69 x3 + 0.30 x4 salary = 17.85 + 1.10 x1 + 0.32 x2 + 1.59 x3 + 1.29 x4
The data regarding the production of wheat in tons (X) and the price of the kilo of flour in Ghana cedis (Y) Takoradi some years ago were: a. Fit the regression line for the day using the method of least squares
A regression analysis between weight (y in pounds) and height (x in inches) resulted in following least squares line: y^= 120+5x. this implies that if the height is increased by 1 inch, the weight is expected ?
An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas use y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65F) over a 23-month period. He then computed the least squares regression line for predicting y from x and found it to be, ŷ=85+16x How much, on average, does gas used increase for each additional degree-day? The predicted amount of gas used when the outside temperature is 20 degree- days.
For a least squares regression line, the sum of the residuals is __________. always negative sometimes positive and sometimes negative always zero always positive

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