Publications by Ahmed Elsaeyed
AElsaeyed_Homework15
Question 1 Find the equation of the regression line for the given points. Round any final values to the nearest hundredth, if necessary. ( 5.6, 8.8 ), ( 6.3, 12.4 ), ( 7, 14.8 ), ( 7.7, 18.2 ), ( 8.4, 20.8 ) Using least squares method, the formulas for the slope \(m\) and the y-intercept \(b\) are given by: \[ m = \frac{n\sum (xy) - \sum x \sum y}{...
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AElsaeyed_Discussion15
Page 711 Question 5 Evaluate \(f(x, y) = x^2y - x + 2y + 3\) at (1,2). The partial derivatives: \[ f(x, y) = x^2y - x + 2y + 3 \] Compute \(f_x(x, y)\): \[ f_x(x, y) = \frac{\partial}{\partial x} (x^2y - x + 2y + 3) \] Applying the derivative: \[\begin{align*} \frac{\partial}{\partial x} (x^2y) &= 2xy, \\ \frac{\partial}{\partial x} (-x) &= -1, \\ ...
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AElsaeyed_Homework14
Taylor Series Expansion • f (x) =1/ (1−x) • f (x) = e^x • f (x) = ln(1 + x) • f(x)=x^(1/2) For each function, only consider its valid ranges as indicated in the notes when you are computing the Taylor Series expansion. Please submit your assignment as an R- Markdown document. 1) \[ f(x) = \frac{1}{1-x} \] Starting with the derivatives of...
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AElsaeyed_Discussion14
Page 496 Question 25 Use the Taylor series given in Key Idea 8.8.1 to create the Taylor series of the given functions: \[ \cos(x^2) \] From Key Idea 8.8.1: The standard Taylor series expansion for \(\cos x\) is: \[ \cos x = \sum_{n=0}^{\infty} (-1)^n \frac{x^{2n}}{(2n)!} \] By substituting \(x^2\) for \(x\), we derive the series for \(\cos(x^2)\): ...
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AElsaeyed_Discussion12
Using R, build a multiple regression model for data that interests you. Include in this model at least one quadratic term, one dichotomous term, and one dichotomous vs. quantitative interaction term. Interpret all coefficients. Conduct residual analysis. Was the linear model appropriate? Why or why not? https://www.kaggle.com/datasets/prakharrathi...
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AElsaeyed_Homework12
Question 1 Provide a scatterplot of LifeExp~TotExp, and run simple linear regression. Do not transform the variables. Provide and interpret the F statistics, R^2, standard error,and p-values only. Discuss whether the assumptions of simple linear regression met. Download the Data my_git_url <- getURL("https://raw.githubusercontent.com/AhmedBuckets/...
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Document
Download the Data my_git_url <- getURL("https://raw.githubusercontent.com/AhmedBuckets/SPS605/main/home_data.csv") price_data <- read.csv(text = my_git_url) Plotting Price against Square Feet Make Model price_sqft_model <- lm(price ~ sqft_living, data = price_data) Display Line of Best Fit ## integer(0) Look at the Summary ## ## Call: ## lm(f...
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AElsaeyed_Homework11
Plotting the Data Fit a Linear Model I used the lm function to find the relationship between stopping distance and speed as a linear model. model <- lm(dist ~ speed, data = cars) Display Line of Best Fit ## integer(0) Look at the Summary ## ## Call: ## lm(formula = dist ~ speed, data = cars) ## ## Residuals: ## Min 1Q Median 3Q...
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AElsaeyed_Discussion9
Page 36 Question 12 Test your conclusions in Exercise 11 by computer simulation. First choose 364 numbers Xi with density f(x) = normal(x, 0, 1/4). Now form the sum Y365 = 100 + X1 + X2 + · · · + X364, and repeat this experiment 200 times. Make up a bar graph on [50, 150] of the results, superimposing the graph of the approximating normal densit...
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AElsaeyed_Homework9
Question 1 The price of one share of stock in the Pilsdorff Beer Company (see Exercise 8.2.12) is given by \(Y_n\) on the nth day of the year. Finn observes that the differences \(X_n = Y_{n+1} − Y_n\) appear to be independent random variables with a common distribution having mean µ = 0 and variance \(σ^2\) = 1/4. If \(Y_1\) = 100, estimate th...
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