首页 >
> 详细

Stat 315: HW #11

Fall 2019

Due: Wednesday, December 4, 2019

1. An engineer is attempting to model the potential energy of a spring based on the displacement

from equilibrium of the spring. The experimental data is provided below.

x (displacement) 1 2 3 4 5

y (potential energy) 2.23 3.62 6.77 13.47 21.06

(a) Make a scatterplot of the data by hand. Comment on whether there appears to be a

linear relationship, a nonlinear relationship, or no apparent relationship.

(b) Compute the estimated regression equation by hand and sketch the line of best fit on

your scatterplot.

(c) Verify the estimated regression equation in R.

(d) Make a plot of the fitted values versus the residuals in R. Is there evidence that the

relationship is not linear? Explain.

2. The engineer suspects that there is a quadratic relationship between potential energy and

displacement. Let z = x

z (squared displacement) 1 4 9 16 25

y (potential energy) 2.23 3.62 6.77 13.47 21.06

(a) Use R to find the estimated regression equation, i.e., ˆy = b0 + b1z = b0 + b1x

(b) Using the R output, construct a 95% confidence interval for β1. Is there evidence that

β1 differs from zero? Explain.

(c) Use R to create an ANOVA table. Once you have created the ANOVA table, use it to

calculate R2 and interpret R2

in the context of the problem.

(d) What is the correlation between z and y?

(e) Complete a six-step hypothesis test to determine if there is linear relationship between

z and y at α = 0.01.

3. American astronomer, Edwin Hubble, discovered in 1929 that there was a relationship

between the relative velocity (km/sec as measured from Earth) of celestial objects (such as

stars and nebulae) and their distance (Mpc, megaparsec) from Earth. This led Hubble to

conclude that the universe must be expanding. “Hubble’s Law” states that celestial objects

tend to have a “redshift” Doppler effect and this was the result of an expanding universe.

This problem will examine Hubble’s original dataset.

(a) Download “hubble.csv” from Canvas and load it into R Studio using File > Import

Dataset > From Text (base).

Once you have loaded the dataset, run the command “head(hubble)” to see some of the data

values. What is the velocity and distance of the first data value?

(b) Using R, fit a simple linear regression model with distance (Mpc) as the predictor variable

and velocity (km/s) as the response variable. What is the estimated regression equation

and what velocity does it estimate for an object 1 Mpc from Earth?

(c) Is there evidence of a linear relationship? Conduct a six-step hypothesis test at α = 0.05.

(d) Use R to make a scatterplot with the estimated regression equation. Hint: once you

have fit your model (suppose it is called “mod”), run the command “abline(mod)” to add

the line of best fit.

(e) Construct a simultaneous 95% confidence band for mean response. Suppose it is claimed

that the mean velocity of an object 1 Mpc from Earth is 800 km/s. Using your plot, at

α = 0.05, would you reject or fail to reject this hypothesis?

(f) Construct a simultaneous 95% prediction band for a new data value. About 95% of the

the data values should fall within these bands. What percent of the data values fall inside

these bounds?

(g) Construct a plot of the fitted values versus the residuals. Is there evidence of nonconstant

variance or a nonlinearity? Explain.

(h) Construct a QQ-plot. Is there evidence that the errors are not normally distributed?

Explain.

4. For the Hubble example, ¯x = 0.91125, MSE = 54382, Sxx = 9.59, and n = 24.

(a) Compute a 95% confidence interval for mean response for Distance = 1 Mpc. Suppose

it is claimed that the mean velocity for an object at 1 Mpc is 800km/s. Would you reject or

fail to reject this claim? Explain.

(b) Compute a 95% prediction interval for a new data value for Distance = 1 Mpc. Is it

plausible that an object that is 1 Mpc from Earth has a velocity of 0 km/s relative to Earth? Explain.

联系我们

- QQ：99515681
- 邮箱：99515681@qq.com
- 工作时间：8:00-23:00
- 微信：codinghelp

- 代写cs3014 Google Analytics Customer Rev 2020-01-21
- 代写cmpsc121 Structs代写留学生c/C++实验... 2020-01-21
- 代写mis6326 Data Management调试存储过程作业、数据库编 2020-01-21
- 代写msci 581作业、代做marketing Analytics作业、P 2020-01-20
- Software课程作业代做、代写java，C/C++程序设计作业、Pyth 2020-01-20
- Tcss 372作业代做、代写python，Java编程语言作业、代做c/C 2020-01-20
- Emergency Facilities作业代写、代写r编程设计作业、R课程 2020-01-18
- Cis 413/513作业代做、代写data Structures作业、Ja 2020-01-18
- 代写ia626留学生作业、Python程序设计作业调试、代做data课程作业 2020-01-18
- Mat00027i作业代写、Java程序语言作业调试、Mathematica 2020-01-17
- 代做kt Model作业、代写java，Python编程设计作业、代做c/C 2020-01-17
- Data Set课程作业代做、代写r程序语言作业、Ltcret留学生作业代做 2020-01-17
- 代写rstudio留学生作业、代做r编程设计作业、代写r课程设计作业代做数据 2020-01-17
- 代写cs2250 Delimiter Matching代做数据结... 2020-01-16
- 代写cs12b Edit Distance帮写java实验作业... 2020-01-16
- 代写mins325 Filereader And Filewriter代... 2020-01-16
- 代写cosi131 Tunnels帮写java实验作业 2020-01-16
- 代写inm312 Balancebit Software代写留学... 2020-01-16
- 代写cs61b Maze Solver代写java课程设计 2020-01-16
- Program留学生作业代做、C/C++编程语言作业代写、代做java，Py 2020-01-14