4. A certain working device (operated by cycling) that is specialized in food slicing has been suspected of producing thicker slices the higher the price per kilogram of that product is. Such behaviour makes the users of the device curious, so let's look at the situation using a linear model. Suppose that for all i = 1, . . ., n, the thickness (in mm) of the measured slices is represented by y; and their corresponding random variables satisfy Y₁ = ẞxi + Ei, ~ 3 N(0,σ²), where ẞER and σ² > 0 are unknown parameters and x; are know values of ex- planatory variables (the price per kilogram of selected item). Under strictly controlled conditions is obtained the following data was obtained Xi 12.40 9.17 4.10 15.47 23.68 18.18 4.75 23.19 32.46 7.49 Yi 8.17 6.65 2.75 10.75 16.71 12.04 4.72 11.75 18.07 4.83 Using the formulas in lecture notes and results in Chapter 9 (a) Create an ML estimate (using the OLS (ordinary least squares, PNS, pienin neliösumma) method, p. 106) for the parameter ß. (b) What is the standard error of the ML estimate of the slope? Draw (either by hand or with R, for example) a scatterplot where the explaining variables are on the x-axis and the responses are on the y-axis. Draw an OLS line (corresponding to the ML estimates for the parameters a and ẞ) in the scatterplot you have drawn.
4. A certain working device (operated by cycling) that is specialized in food slicing has been suspected of producing thicker slices the higher the price per kilogram of that product is. Such behaviour makes the users of the device curious, so let's look at the situation using a linear model. Suppose that for all i = 1, . . ., n, the thickness (in mm) of the measured slices is represented by y; and their corresponding random variables satisfy Y₁ = ẞxi + Ei, ~ 3 N(0,σ²), where ẞER and σ² > 0 are unknown parameters and x; are know values of ex- planatory variables (the price per kilogram of selected item). Under strictly controlled conditions is obtained the following data was obtained Xi 12.40 9.17 4.10 15.47 23.68 18.18 4.75 23.19 32.46 7.49 Yi 8.17 6.65 2.75 10.75 16.71 12.04 4.72 11.75 18.07 4.83 Using the formulas in lecture notes and results in Chapter 9 (a) Create an ML estimate (using the OLS (ordinary least squares, PNS, pienin neliösumma) method, p. 106) for the parameter ß. (b) What is the standard error of the ML estimate of the slope? Draw (either by hand or with R, for example) a scatterplot where the explaining variables are on the x-axis and the responses are on the y-axis. Draw an OLS line (corresponding to the ML estimates for the parameters a and ẞ) in the scatterplot you have drawn.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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Transcribed Image Text:4. A certain working device (operated by cycling) that is specialized in food slicing has
been suspected of producing thicker slices the higher the price per kilogram of that
product is. Such behaviour makes the users of the device curious, so let's look at
the situation using a linear model. Suppose that for all i = 1, . . ., n, the thickness
(in mm) of the measured slices is represented by y; and their corresponding random
variables satisfy
Y₁ = ẞxi + Ei,
~ 3
N(0,σ²),
where ẞER and σ² > 0 are unknown parameters and x; are know values of ex-
planatory variables (the price per kilogram of selected item). Under strictly controlled
conditions is obtained the following data was obtained
Xi 12.40 9.17 4.10 15.47 23.68 18.18 4.75 23.19 32.46 7.49
Yi
8.17 6.65 2.75 10.75 16.71 12.04 4.72 11.75 18.07 4.83
Using the formulas in lecture notes and results in Chapter 9
(a) Create an ML estimate (using the OLS (ordinary least squares, PNS, pienin
neliösumma) method, p. 106) for the parameter ß.
(b) What is the standard error of the ML estimate of the slope?
Draw (either by hand or with R, for example) a scatterplot where the explaining
variables are on the x-axis and the responses are on the y-axis. Draw an OLS
line (corresponding to the ML estimates for the parameters a and ẞ) in the
scatterplot you have drawn.
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