MATLAB: A Practical Introduction to Programming and Problem Solving
5th Edition
ISBN: 9780128163450
Author: ATTAWAY
Publisher: ELSEVIER
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Chapter 13, Problem 11E
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The following three independent random samples are obtained from three normally distributed
populations. The (dependent) numerical variable being compared is starting hourly wage, and the groups
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Click Download CSV to download csv file of data or copy/paste the data into Excel. After downloading the
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Use Excel to conduct a one-way ANOVA to determine if the group means are equal using a = 0.05.
Create a side-by-side boxplot in Excel for these data. Use that and the numerical summary of sample data
to answer the following questions.
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a. Which group has the highest average?
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Two sample t tests are limited to situations in which there are only
compared.
The Analysis of Variance (ANOVA) is used to tests where
being compared in one hypothesis test.
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Dak is investigating how long their phone's battery lasts (in hours) for various brightness levels (on a scale
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A part of the regression analysis done on Ti Calculator and in Excel for their data are displayed below.
Ti Calculator
Click this button to reveal the Ti Calculator Output. Click again to collapse it.
Ti Calculator
y = ax+b
B0 and p 0
t = -3.02431335
p = 0.0233
df - 6
a =-0.0380555845
b=5.88809202
s = 0.436054238
20.603868129
r = -0.777089524
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Click this button to reveal the Excel Output. Click again to collapse it.
SUMMARY OUTPUT
Multiple R
0.777089524
R Square
0.603868129
Adjusted R Square
0.537846150
Standard Error
0.436054238
Observations
8
ANOVA
df
SS
MS
F
Significance F
Regression
1
1.73914021
Residual
6
1.14085979
1.73914021
0.190143298
9.1465
0.0233
Total
7
2.88000000
Coefficients
Standard Error
Intercept
Brightness
5.88809202
-0.0380555845
t Stat
7.62593816
-3.02431335
P-value
0.0003
0.0233
Use…
Chapter 13 Solutions
MATLAB: A Practical Introduction to Programming and Problem Solving
Chapter 13, Problem 13.2PChapter 13, Problem 13.3PChapter 13, Problem 13.4PChapter 13, Problem 1EChapter 13, Problem 3EChapter 13, Problem 6EChapter 13, Problem 7EChapter 13, Problem 8EChapter 13, Problem 9EChapter 13, Problem 10E
Chapter 13, Problem 11EChapter 13, Problem 13EChapter 13, Problem 14EChapter 13, Problem 15EChapter 13, Problem 16EChapter 13, Problem 17EChapter 13, Problem 19EChapter 13, Problem 21EChapter 13, Problem 23EChapter 13, Problem 24EChapter 13, Problem 25EChapter 13, Problem 26EChapter 13, Problem 28EChapter 13, Problem 29EChapter 13, Problem 34EChapter 13, Problem 35E
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- ce Problems x + canvas.pdx.edu/courses/106252/assignments/1102408?module_item_id=4856656 m Proctor ments THIS IS THE second question of exdin where you have to Snow compere work to get run points. If you use TI calculator functions, you may write your work along with functions and values you I used and answers on a paper or type on an empty Word document or Excel file. If you use Ti calculator app on your computer or phone, you may provide screen shots of those on a word document or Excel file. Clearly provide the function along with values for the work. If you use Excel, you may use the Excel calculator or Excel as a calculator on your computer to provide complete work and the final answer on it. Please provide all the answers to the following questions on the same Excel sheet. If you use formula, you may write all your steps with numbers on a paper and submit a photo of it. Otherwise, you may type all those steps on a Word document or an Excel file. Do NOT round in the middle steps…arrow_forwardSuppose the model for certain data is a parabola y = Bo+B1x+B2x² with observations (1, 2.2), (2, 6.9), (3, 16.1), (4, 28.7), (5, 46.1). Describe the design matrix, the observation vector, and the parameter vector. Using these write down the system of equations to be approximated Xẞ = y, the parts of the normal equations XTX and XTy and write down the normal equations. Solve and determine the residual vector €. You may use a calculator for the computations but show the steps as described above.arrow_forward. This problem will yield a standard formula given in elementary statistics for a least squares line, making use of the normal equations. (a) Given pairs of data points (x1, Y1), (x2, Y2), ..., (xn, Yn) consider approximating lines of the form y = mx+b. The error e; for the ith pair is the distance between y; and the height (y value) of the line at xi. This is ei = Yi — (mxi + b). If we consider the equations b + x;m = Yi for i n in the variables b and m we can = 1,2, = think of this as a system of equations Ax = 6 where A 1 x1 x2 = : [m] Хп Y1 Уп numbers. Here, note that the variables are m and b and the xi, Yi are given The least squares approximation for this system (which gives the intercept b and slope m of the best least squares line for the data) is the solution to the normal equations AT Ax = ATb. Determine ATA (a 2×2 matrix) and AT (a 2×1 matrix). The entries will be sums of terms involving the x; and y₁. Write these, first using Σ notation and then simplify the notation using…arrow_forward
- = a) Recall that the formula for the projection p of vector & onto vector a is p = ±ªã. The plane through the origin in R³ given by ax+by+cz = 0 for real numbers a, b, c, is the set of all points (viewed as vectors) orthogonal to the normal n = (a, b, c) to the plane. To find the distance from a point w (xo, Yo, zo) to the plane ax+by+cz = 0 we can find the projection of w onto the normal ñ and then find the length of this projection. Do this to derive a generic formula for the distance in terms of xo, Yo, Zo, a, b, c. First find the length squared and then take a root. b) To find the distance from a point w (xo, Yo, zo) to a plane ax + by + cz = d, not necessarily not through the origin, one approach is to shift all z coordinates down by d. That is, replace (x, y, z) by (x, y, z — d). The relationship between the plane and w is unchanged so we can find the distance by finding the distance between (xo, Yo, zo - d) and the plane ax + by+cz = 0 through the origin. Do this to derive a…arrow_forwardUse Gram-Schmidt orthogonalization to find an orthonormal set of vectors with the same span as = 1 2 -0-08-0 a2 = 3 a3 = -2 Find also a QR factorization A = QR with the columns of Q the orthonormal set found above and R upper triangular and invertible and A with columns ā₁, ā2, ā3.arrow_forward(a) Let Q be an orthonormal matrix. That is, the columns of Q have unit length and are pairwise orthogonal. Prove that the length of Qã is equal to the length of for any column vector x. Note that you can do this by showing that the lengths squared are equal. (b) Prove that if A and B are symmetric and πT Ax = x² Bã for all & then A = B. Make use of coordinate vectors ē;, which are 0 except for a 1 in position i. Explain why, for matrix A, entries can be found by arj = Aej. First show that diagonal = = entries aii bir. Then consider what (ē¿ + ē¿)ªA(ē¿ + ē¿) in terms of entries of A (and similarly for B) and make use of symmetry aij = aji and similarly for B. (c) Prove the converse: If for all x, ||Q|| ||||| then Q is orthonormal. One ap- proach is to use part (b) to show that QTQ = I. Recall that QTQ is symmetric (and trivially I is symmetric). Recall also that, written in matrix notation, vector length (squared) is given by ||7||2 = (this is the dot product written in matrix…arrow_forward
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- Please could you provide solutions to the following questions. Thanksarrow_forwardor Beer and blood alcohol content: Many people believe that gender, weight, drinking habits, and many other factors are much more important in predicting blood alcohol content (BAC) than simply considering the number of drinks a person consumed. Here we examine data from sixteen student volunteers at Ohio State University who each drank a randomly assigned number of cans of beer. These students were evenly divided between men and women, and they differed in weight and drinking habits. Thirty minutes later, a police officer measured their blood alcohol content (BAC) in grams of alcohol per deciliter of blood (Malkevitc and Lesser, 2008). The scatterplot and regression table summarize the findings. to search BAC (grams per deciliter) 0.15- 0.10- 0.05- Part of Ti Calculator Output Ti Calculator y = ax+b Be and p = 0 t = 7.48 P 0.0000 df = 14 a = 0.0180 b = -0.0127 Part of Excel Output 2 4 0 0 6 Cans of beer (Intercept) beers Estimate -0.0127 0.0180 Std. Error t value 0.0126 P(>|t|) -1.00…arrow_forwardProctor ts Ces rces arch Question 31 The data below was collected from manufacturer advertisements of their vehicles horsepower (x) and highway gas mileage (mpg=y). Use this data to answer the following questions. horsepower 157 250 340 350 390 190 220 mpg 33 28 15 17 11 35 42 1. Find the p-value to determine if there is a linear correlation between horsepower and highway gas mileage (mpg). Record the p-value below. Round to four decimal places. p-value= 2. Is there a linear correlation between horsepower and highway gas mileage (mpg)? ? 3. If there is a linear correlation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places. Be careful with your sign. T= 4. If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places. ŷ 5. Using the data shown above, predict the the highway gas mileage (mpg) for a car that has a horsepower of 225. Round your…arrow_forward
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