STAT 200-010讲解、Python，c++程序讲解、辅导Java编程语言
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Penn State University
STAT 200-010
Fall 2020
Second Midterm Exam
Thursday October 29th
, 2020 (8:25 AM – 10:20 AM)
Student Name:
ID:
Do not write anything in this table; this is for grader use only!
Question: 1
(a) (5 Pts.) What is meant by a scatter plot?
(b) (5 Pts.) Define the term “Time Plot”.
(c) (10 Pts.) Use Excel to calculate the correlation factor of the following data:
(d) (5 Pts.) Once you have calculated the correlation factor in “c” determine its “Direction”,
“Form”, and “Strength”.
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Question: 2
You are given the following data set:
X Y
1.2 3.6
2.4 7
3.1 9.5
4.5 13.8
5.6 17.2
This data set has a correlation factor 𝑟 = 0.9996. Do not use Excel in this question and show
your calculations in detail for full credit.
(b) (5 Pts.) Calculate the standard deviations 𝑆𝑥 = √.
(c) (5 Pts.) Calculate the slope 𝑏1 = 𝑟𝑆𝑦𝑆𝑥.
(d) (5 Pts.) Calculate the y-intercept 𝑏0 = 𝑦̅ − 𝑏1𝑥̅.
(e) (5 Pts.) Write down the linear regression equation 𝑦̂ = 𝑏0 + 𝑏1𝑥 (you need to substitute
numerical values for 𝑏0 and 𝑏1).
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Question: 3
You are presented with the following data set:
X Y 𝑦̂ Residuals
1 5.2
2 10.6
3 16.1
4 22.3
5 27.8
Do not use Excel for this question.
(a) (15 Pts.) Given that the linear-regression equation for the data set above is
𝑦̂ = 5.69𝑥 − 0.67, calculate 𝑦̂ (the predicted values of y according to the given
regression equation) and the residuals and fill them in the table above:
(b) (5 Pts.) Define “Extrapolation”.
(c) (5 Pts.) Use extrapolation to calculate 𝑦̂(7).
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Question: 4
A factory produces 3 different products, product A, product B, and product C. The table below
shows the total monthly cost (for 5 different months) sustained by the factory to produce a given
count of each product. Here are the data:
Month Total Factory
Cost (in $)
Product A Product B Product C
1 44439 515 541 711
2 43936 929 692 824
3 44464 800 710 758
4 41533 979 675 635
5 46343 1165 1147 901
(a) (20 pts.) Using Excel calculate the multiple-regression equation.
(b) (5 Pts.) Once you have derived that equation, use it predict the total cost sustained by the
factory to produce 300, 400, and 500 counts of the A, B, and C products, respectively.