Equation For Standard Error Of Slope
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Standard Error Of Slope Definition
Notation Share with Friends Hypothesis Test for Regression Slope This lesson describes how to conduct a hypothesis test to determine whether there is a significant linear relationship between an
Standard Error Of Slope Linear Regression
independent variable X and a dependent variable Y. The test focuses on the slope of the regression line Y = Β0 + Β1X where Β0 is a constant, Β1 is the slope (also called the regression coefficient), X is the value of the independent variable, and Y is the value of the dependent variable. If we find that the slope of standard error of slope of regression line the regression line is significantly different from zero, we will conclude that there is a significant relationship between the independent and dependent variables. Test Requirements The approach described in this lesson is valid whenever the standard requirements for simple linear regression are met. The dependent variable Y has a linear relationship to the independent variable X. For each value of X, the probability distribution of Y has the same standard deviation σ. For any given value of X, The Y values are independent. The Y values are roughly normally distributed (i.e., symmetric and unimodal). A little skewness is ok if the sample size is large. Previously, we described how to verify that regression requirements are met. The test procedure consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. State the Hypotheses If there is a significant linear relationship between the independent variable X and the dependent variable Y, the slope will not equal zero. H0: Β1 = 0 Ha: Β1 ≠ 0 The null hypothesis states that the slope is
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Standard Error Of Slope Calculator
about hiring developers or posting ads with us Cross Validated Questions Tags Users Badges Unanswered standard error of slope interpretation Ask Question _ Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data standard error of slope coefficient visualization. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top How is the formula for http://stattrek.com/regression/slope-test.aspx?Tutorial=AP the Standard error of the slope in linear regression derived? [duplicate] up vote 3 down vote favorite This question already has an answer here: Derive Variance of regression coefficient in simple linear regression 2 answers As stated in many textbooks, the Standard error of the slope in linear regression with one variable is $\sqrt{\frac{s^2}{SSX}}$ or some rewrite, ${s^2}$ being the error variance and ${SSX}$ being the sum of the ${x}$-squares. Can anybody help with an explicit proof? regression http://stats.stackexchange.com/questions/91750/how-is-the-formula-for-the-standard-error-of-the-slope-in-linear-regression-deri standard-error share|improve this question edited Apr 14 '14 at 7:05 asked Mar 28 '14 at 20:11 user3451767 11319 marked as duplicate by gung, Nick Stauner, Momo, COOLSerdash, Glen_b♦ Mar 29 '14 at 8:00 This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question. 1 see stats.stackexchange.com/questions/88461/… –TooTone Mar 28 '14 at 23:19 It's reasonably straightforward if you start from the fact that the line goes through $(\bar x,\bar y)$ and write the slope estimator as a kind of average. –Glen_b♦ Mar 29 '14 at 0:01 Thx. Answer 1 to stats.stackexchange.com/questions/88461/… helped me perfectly. –user3451767 Apr 9 '14 at 9:50 add a comment| 2 Answers 2 active oldest votes up vote 4 down vote To elaborate on Greg Snow's answer: suppose your data is in the form of $t$ versus $y$ i.e. you have a vector of $t$'s $(t_1,t_2,...,t_n)^{\top}$ as inputs, and corresponding scalar observations $(y_1,...,y_n)^{\top}$. We can model the linear regression as $Y_i \sim N(\mu_i, \sigma^2)$ independently over i, where $\mu_i = a t_i + b$ is the line of best fit. Greg's way is to use vector notation. We can rewrite the above in Greg's notation: let $Y = (Y_1,...,Y_n)^{\top}$, $X = \left( \begin{array}{2} 1 & t_1\\ 1 & t_2\\ 1 & t_3\\ \vdots \\ 1 & t_n \end{array} \right)$, $\b
in Excel (Linear Regression in Physics Lab) January 4, 2013 by Jeff Finding Standard Error of Slope and Y-Intercept using LINEST in Excel (Linear Regression in Physics Lab) In Excel, you can apply a line-of-best fit to any scatterplot. The equation for the fit can be displayed but the http://www.fiz-ix.com/2013/01/finding-standard-error-of-slope-and-y-intercept-using-linest-in-excel-linear-regression-in-physics-lab/ standard error of the slope and y-intercept are not give. To find these statistics, use the LINEST function instead. The LINEST function performs linear regression calculations and is an array function, which means that it returns more than one value. Let's do an example to see how it works. Let's say you did an experiment to measure the spring constant of a spring. You systematically varied the force exerted on the spring (F) and measured the amount standard error the spring stretched (s). Hooke's law states the F=-ks (let's ignore the negative sign since it only tells us that the direction of F is opposite the direction of s). Because linear regression aims to minimize the total squared error in the vertical direction, it assumes that all of the error is in the y-variable. Let's assume that since you control the force used, there is no error in this quantity. That makes F the independent value standard error of and it should be plotted on the x-axis. Therefore, s is the dependent variable and should be plotted on the y-axis. Notice that the slope of the fit will be equal to 1/k and we expect the y-intercept to be zero. (As an aside, in physics we would rarely force the y-intercept to be zero in the fit even if we expect it to be zero because if the y-intercept is not zero, it may reveal a systematic error in our experiment.) The images below and the following text summarize the mechanics of using LINEST in Excel. Since it is an array function, select 6 cells (2 columns, 3 rows). You can select up to 5 rows (10 cells) and get even more statistics, but we usually only need the first six. Hit the equal sign key to tell Excel you are about to enter a function. Type LINEST(, use the mouse to select your y-data, type a comma, use the mouse to select your x-data, type another comma, then type true twice separated by a comma and close the parentheses. DON'T HIT ENTER. Instead, hold down shift and control and then press enter. This is the way to execute an array function. The second image below shows the results of the function. From left to right, the first row displays the slope and y-intercept, the second row displays t
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