Q5 Please provide justified answer asap to get a upvote A certain experiment produces the data (1, 1.7), (2, 2.8), (3, 3.3), (4, 3.5), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y=B₁x + ₂x². Such a function might arise, for example, as therevenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product.a. Give the design matrix and observation vector for the unknown parameter vector =b. Find the associated least-squares curve for the data.a. The design matrix is X=The observation vector is y=.b. The least-squares curve for the data is given by the function y=x+x².(Round to two decimal places as needed.)CS Scanned with CamScanner

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Answered: A certain experiment produces the data…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 2ECP

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Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.
A random sample of 65 high school seniors was selected from all high school seniors at a certain high school. A scatterplot (not shown) revealed the height, in cm and foot length in cm, for each high school student from the sample. The association was described to be strong, positive, and linear. a. In the context of the study, explain what is meant by the following terms: positive: linear: b. The least squares regression equation was predicted height=105.08+2.599 (foot length). One of the students had a foot length of 20 cm. His residual was calculated to be 2.94 cm. What was the height of the student? c. suppose that the distribution of residuals is approximately normal with a standard deviation of 5.9 cm. What percent of residuals are less than 7 cm? Justify why.
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.
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 ? (in cubic feet) to heat the home and outside temperature ? (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 ? from ? and found it to be ?̂ =85+16?. By looking at the equation of the least‑squares regression line, you can see that the correlation between amount of gas used and degree‑days is
A lab received a new instrument to measure pH. To compare the new instrument to the old lab instrument, 11 samples were measured with both pieces of equipment. Using the data (below), find the least squares equation (x = "pH old" and Y = "pH new") and then predict the value on the new instrument if the old instrument gave a pH of 6.30. Enter your answer using 3 significant digits. pH Old pH New 6.35 6.16 6.01 5.95 6.15 6.05 6 6.01 6.11 6.06 5.93 5.83 5.84 5.81 5.63 5.71 5.63 5.74 6.11 6.1 6.07 6.01
Consider the one-variable regression model Yi = β0 + β1Xi + ui, and suppose it satisfies the least squares assumptions in Key Concept 4.3. Suppose Yi is measured with error, so the data are ?"i = Yi + wi, where wi is the measurement error, which is i.i.d. and independent of Yi. Consider the population regression ?"i = β0 + β1Xi + vi, where vi is the regression error, using the mismeasured dependent variable ?"i.a) Showthatvi =ui +wi.b) Show that the regression ?"i = β0 + β1Xi + vi satisfies the least squares assumptions in KeyConcept 4.3. (Assume that wi is independent of Yj and Xj for all values of i and j and has afinite fourth moment.)c) Are the OLS estimators consistent? part b in another question
A study of IT companies has found the following data on the age of each company and its annual volume of sales: Age (years) Sales (000) 2 22 2.5 34 3 33 4 37 4.5 40 4.5 45 5 49 3 30 6 58 6.5 58 (a) Determine the least squares regression that relates the age of company variable to the sales variable in the form y = a + bx. (b) Provide a practical interpretation of the coefficients a and b. (c) Determine the ‘goodness of fit’ (R2) of the estimated regression line. d) Using the estimated regression line determined in (a), calculate what volume of sales would be predicted for a company that is 3.5 years of age. (e) If it was found that…
A prospective MBA student would like to examine the factors that impact starting salary upon graduation and decides to develop a model that uses program per-year tuition as a predictor of starting salary. Data were collected for 37 full-time MBA programs offered at private universities. The least squares equation was found Y = -13258.594 + 2.422X,, where X; is the program per-year tuition and Y; is the predicted mean starting salary. To perform a residual analysis for these data, the following results are obtained. of regression have been seriously violated. Residual index plot QQ Plot of Residuals Residuals Residuals 20000 20000 -20000 -20000 -40000 40000 TO 20 Index Normal Quantile Residuals vs. Program Per-Year Tuition ($) Residuals Predicted Values vs. Residuals Predicted Values 20000 140000- 120000- 100000 80000- -20000 60000 -40000 40000- 30000 50000 4000 Program Per-Year Tuition ($) 20000 60000 70000 -20000 20000 Residuals ..... a) To evaluate whether the assumption of linearity…

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