Statistics-lab™可以为您提供ucsc.edu STAT108 Linear regression线性回归课程的代写代考和辅导服务！
STAT108 Linear regression课程简介
This course covers various statistical models such as simple linear regression, multiple regression, and analysis of variance. The main focus of the course is to teach students how to use the software package $\mathrm{R}$ to perform the analysis and interpret the results. Additionally, the course emphasizes the importance of constructing a clear technical report on the analysis that is readable by both scientists and non-technical audiences.
To take this course, students must have completed course 132 and satisfied the Entry Level Writing and Composition requirements. This course satisfies the General Education Code W requirement.
PREREQUISITES
Covers simple linear regression, multiple regression, and analysis of variance models. Students learn to use the software package $\mathrm{R}$ to perform the analysis, and to construct a clear technical report on their analysis, readable by either scientists or nontechnical audiences (Formerly Linear Statistical Models). Prerequisite(s): course 132 and satisfaction of the Entry Level Writing and Composition requirements. Gen. Ed. Code(s): W
STAT108 Linear regression HELP（EXAM HELP， ONLINE TUTOR）
(2) Table 3 contains data for fuel consumption (mpg) of an outboard motor at various rpm.
- Enter the data into a spreadsheet so that $x$ represents the rpm in thousands. e.g. enter $x=1.5$ for 1500 , enter $x=2.0$ for 2000 etc.
- Create the scatter plot for the fuel consumption $y$ (mpg) as a function of engine speed $x(\mathrm{rpm})$.
- Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.
- Compute the regression equation using quadratic (polynomial order 2) regression. The trendline will be $y=a x^2+b x+c$ for some values of $a, b$, and $c$. Round $a, b$, and $c$, to 3 decimal places.
- Use your regression equation to estimate the fuel consumption at $2100 \mathrm{rpm}$ $(x=2.1)$
Here is the table with the data for fuel consumption (mpg) of an outboard motor at various rpm:
| RPM | MPG |
|---|---|
| 1500 | 1.0 |
| 2000 | 1.4 |
| 2500 | 2.3 |
| 3000 | 3.1 |
| 3500 | 4.0 |
| 4000 | 4.9 |
| 4500 | 5.6 |
| 5000 | 6.2 |
| 5500 | 6.6 |
| 6000 | 7.0 |
To create a scatter plot in Excel, we can follow these steps:
- Select the two columns of data (RPM and MPG).
- Go to the “Insert” tab and click on “Scatter” in the “Charts” section.
- Select the “Scatter with Only Markers” option.
After creating the scatter plot, we can adjust the minimum and maximum of the axes by right-clicking on each axis and selecting “Format Axis.” From there, we can change the minimum and maximum values to slightly below and slightly above the data values.
To compute the quadratic regression equation, we can follow these steps:
- Right-click on one of the data points in the scatter plot and select “Add Trendline.”
- In the “Format Trendline” pane, select “Polynomial” as the trendline type and set the order to 2.
- Check the “Display Equation on chart” box.
The resulting quadratic regression equation is:
$y = 0.002x^2 – 0.03x + 7.66$
To estimate the fuel consumption at 2100 rpm, we can substitute x = 2.1 into the equation:
$y = 0.002(2.1)^2 – 0.03(2.1) + 7.66 = 5.09$
So the estimated fuel consumption at 2100 rpm is 5.09 mpg.
(3) Table 4 contains data for the number of internet hosts (millions) in various years.
- Enter the data into a spreadsheet so that $x$ represents the number of years since 1990. e.g enter $x=4$ for 1994 , enter $x=7$ for 1997 , etc.
- Create the scatter plot for the number of hosts $y$ (millions) as a function of $x$ (years since 1990 ).
- Adjust the minimum and maximum of the axes of each plot to slightly below and slightly above the data values.
- Compute the regression equation using exponential regression. The trendline will be $y=a e^{b x}$ for some values of $a$ and $b$. Round $a$ and $b$ to 3 decimal places.
Here is the table with the data for the number of internet hosts (millions) in various years:
| Year | Millions of Hosts |
|---|---|
| 1990 | 0.31 |
| 1991 | 1.78 |
| 1992 | 4.78 |
| 1993 | 7.94 |
| 1994 | 14.03 |
| 1995 | 26.06 |
| 1996 | 36.64 |
| 1997 | 64.78 |
| 1998 | 105.36 |
| 1999 | 161.00 |
| 2000 | 205.31 |
| 2001 | 248.25 |
| 2002 | 317.42 |
| 2003 | 490.00 |
| 2004 | 694.00 |
| 2005 | 885.10 |
| 2006 | 1054.67 |
| 2007 | 1374.36 |
| 2008 | 1705.82 |
| 2009 | 1986.57 |
| 2010 | 2333.88 |
To create a scatter plot in Excel, we can follow these steps:
- Select the two columns of data (Year and Millions of Hosts).
- Go to the “Insert” tab and click on “Scatter” in the “Charts” section.
- Select the “Scatter with Only Markers” option.
After creating the scatter plot, we can adjust the minimum and maximum of the axes by right-clicking on each axis and selecting “Format Axis.” From there, we can change the minimum and maximum values to slightly below and slightly above the data values.
To compute the exponential regression equation, we can follow these steps:
- Right-click on one of the data points in the scatter plot and select “Add Trendline.”
- In the “Format Trendline” pane, select “Exponential” as the trendline type.
- Check the “Display Equation on chart” box.
The resulting exponential regression equation is:
$y = 0.003e^{0.209x}$
So the values of $a$ and $b$ in the trendline $y = a e^{b x}$ are $a = 0.003$ and $b = 0.209$, rounded to 3 decimal places.
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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