本次数学辅导的主要内容是回归模型计算
Math1312：回归分析
指示
如果您无法参加任何课程，则您有责任在截止日期之前完成此作业。可以在Canvas中找到有关主题1的注释。
强烈建议您参加课程，如果不确定任何问题，请咨询您的讲师/导师。
您必须在画布上在线提交完成的作业（我建议您保留作业的副本（硬拷贝，扫描副本等）。）
4.除非另有说明，否则在需要的地方使用显着性水平a = 5％。
问题1：下表提供了加拿大安大略省13个湖泊的面积（x平方千米）和pH值水平（y）的测量值。 （如果没有其他说明，请手动计算）
面积（x）33161189149 47170352 187 76 5217553200 pH（y）6.6 6.4 6.5 6.9 7.1 7.5 8.8 6.4 5.9 6.7 7.1 6.6 8.0
（a）绘制y vs x的散点图并在该图上发表评论。 （使用Minitab或R / Rstudio）
（b）使用最小二乘原理将简单线性回归模型拟合到数据中。将最佳拟合线叠加在部分（a）的散点图上。
（c）进行ANOVA测试以推断面积与pH值之间是否存在线性关系。
（d）使用R / Rstudio或MINITAB进行所有适当的残差检查，并明确说明是否违反任何模型假设。
（e）在同一地区发现另一个湖泊面积为2050平方公里。预测其pH值并找到该预测的99％置信区间。
（3 + 8 + 5 + 8 + 3 = 27）
问题2 ：（如果另有说明，则需要手动完成的所有操作）提供了以下数据：
其中X表示每月以磅为单位的蒸汽，Y表示以华氏度为单位的平均大气温度。
计算以下内容：
a）拟合线性回归模型并给出最小二乘估计
常数和斜率。
b）分别计算25个观测值的残差。
c）制作方差分析表并通过执行所有必需的步骤来完成
计算。方差分析表有什么用？
d）找到确定系数和相关系数。解释
它的价值。
e）计算误差的标准差，斜率的标准差，以及标准差的标准差
持续的。
f）测试斜率和常数是否有效。陈述需要的
假设并解释您的结果。
g）构造斜率和常数的置信区间。
（8 + 4 + 6 + 4 + 6 + 4 + 6 = 38）
Math1312: Regression Analysis
INSTRUCTIONS
- If you are unable to attend any of the classes, it is your responsibility to complete this assignment before the due date. Notes regarding Topic 1 can be found in Canvas.
- It is strongly recommended that you attend classes and ask your lecturer/tutor if you are unsure of any of the questions.
- You must submit your completed assignment on line in canvas (I recommend you to keep a copy (hardcopy, scanned copy, etc.) of your assignment.)
4. Where needed use a significance level a=5% unless otherwise is stated.
Question 1: The following table gives measurements of the area (x in km2) and pH level (y) of 13 lakes in Ontario, Canada. (hand calculation if nothing else is stated)
Area(x) 33 161 189 149 47 170 352 187 76 52 175 53 200 pH(y) 6.6 6.4 6.5 6.9 7.1 7.5 8.8 6.4 5.9 6.7 7.1 6.6 8.0
- (a) Sketch the scatterplot of y vs x and comment on the plot. (use Minitab or R/Rstudio)
- (b) Use the Principle of Least Squares to fit the simple linear regression model to the data. Superimpose this line of best fit on the scatterplot in part (a).
- (c) Perform an ANOVA test to deduce whether there is a linear relationship between area and pH level.
- (d) Perform all appropriate residual checks using R/Rstudio or MINITAB and clearly explain if any of the model assumptions have been violated.
- (e) Another lake in the same region was found to have an area of 2050 km2 . Predict its pH level and find a 99% confidence interval of this prediction.(3+8+5+8+3=27)
Question 2: (Everything to be done by hand expect if otherwise is stated) The following data are provided:
Where X represent the steam in pounds per months and Y is the mean atmosphere temperature measured in Fahrenheit.
Calculate the followings:
- a) Fit a linear regression model and give the least square estimates for theconstant and the slope.
- b) Calculate the residuals for each of the 25 observations.
- c) Make the ANOVA table and complete it by performing all the requiredcalculations. What is the ANOVA table used for?
- d) Find the coefficient of determination and the correlation coefficient. Explainits value.
- e) Calculate the std for the error, the std for the slope and the std for theconstant.
- f) Test whether the slope and the constant are significant. State the neededhypotheses and explain your results.
- g) Construct the confidence intervals for the slope and for the constant.(8+4+6+4+6+4+6=38)
