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Simple Linear Regression

Simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable. Simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model as small as possible. “Simple” refers to the fact that this regression is one of the simplest in statistics. The slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. The intercept of the fitted line is such that it passes through the center of mass of the data points.

There are three numerical properties of simple linear regression. These are as followed:

  1. The line goes through the “center of mass” points (x(bar), y(bar))
  2. The sum of the residuals is equal to zero, if the model includes a constant
  3. The linear combination of the residuals, in which the coefficients are the x-value, is equal to zero

The description of statistical properties of estimators, from a simple linear regression, estimates require a statistical model. This is based on the assumption of the validity of a model under which the estimates are optimal. It is also possible to evaluate the properties under other assumptions.

U.S. retail trade industry

Average hourly earnings in the U.S. retail trade industry (in current dollars and constant dollars) are shown in the table. Year 1990 1995 2000 2002 2003 Current dollars 4.88 5.94 6.75 7.13 7.29 Constant dollars 5.70 5.39 5.07 5.00 4.97 a. Define the terms current dollars and constant dollars. You will

Chi-square Analysis: Association Strength for the Variables

Using a chi-square analysis, determine the association strength for the variables agecat and degree as well the major contributing cells. Use standardized residuals to determine the cell contributions. • The output of SPSS • Instructions or screen shots on how you did chi-square in SPSS • The report should include chi-s

Drawing Regression Scatterplots

16. Calculate the linear regression equation for each of the situations presented below and draw the regression equation into its scatterplot: a. A researcher hypothesizes a positive relationship between the number of children in a family and the number of televisions a family owns. b. Is there a relationship between t

Evaluating Null Hypotheses

Copy the Assignment Data (i.e., cake mix data) to Sheet 1, cells A1:P32, of a new Excel workbook. Select the most appropriate hypothesis test described in Sections 4.7 and 4.8 to evaluate the following null hypothesis: "Sugar grams" cannot predict "Calories from Fat" in packaged cake mixes. Assume normality and linearity.

Scatterplot, Correlation Coefficient, Linear Regression

See the attachments. The regression equation and the standard error of estimate Stewart Fleishman specializes in the psychiatric aspects of symptom management in cancer patients. Pain, depression, and fatigue can appear as single symptoms, in conjunction with one other symptom, or all together in patients with cancer. You

Linear Regression Analysis on Three Variables

My task is to perform a regression analysis on ten people based upon their scores for 3 variables. The independent variables are extraversion, cognitive skills, and communication ability. The dependent variable is sales performance. Based on this regression analysis, I have to hire 2 people from a listing based upon their scores

Understanding Linear Regressions

Application: Assessment The testing of assumptions, recognition of limitations, and proper use of diagnostics are all necessary elements in the use of multiple linear regression for public health research. All of these elements allow biostatisticians to better assess the results of multiple linear regression models. For th

Simple and Multiple Regressions

3) A company has recently conducted a survey of its employees on their job satisfaction. The survey team wants to find out, among other things, if job satisfaction increases with tenure. The data is in file jobsatis.dta, where the first column has job satisfaction scores (0 - 100; the higher, the more satisfied), the second, num

Conducing a Simple Regression and a Multiple Regression

You work for a company that has a number of take-out pizza stores located in Illinois. You want to produce a model that predicts sales at a location based on the total income of the surrounding neighborhood. This will be used for choosing new locations. The data set pizzasales.dta gives sales (in thousands of dollars) and local

Simple Regression using P-Value Approach

1. Joe's Liquor Store is analyzing its own sales data to determine if the day of the month makes a difference in the volume of liquor sold. For this purpose, 31 single-variable regressions have been run. In Regression 1, daily sales is regressed against a dummy that assigns 1 only to the first day of each month. In Regression 2,

Performing and Interpreting Results in a Simple Regression

Website Your company maintains a corporate website, which is managed for it by an independent company ("Webmedia"). They suggest to you that you should pay to advertise your website on one of the most widely visited sites on the web, site W. As proof that this is worthwhile they give you numbers from another (anonymous) client

Regression/Confidence Intervals for Marketing Department

The marketing department of a large supermarket chain would like to determine the effect of shelf space devoted to pet food on the sales of pet food. A random sample of 12 equal-sized stores was selected, given below. The variables are weekly sales (in hundreds of dollars) and shelf space devoted to pet food (in square feet).

Coefficients/Significance Level for Fuel Efficiency

3. Fuel efficiency We got a sample of 50 used cars sold in an auction and defined the following variables. MPG Fuel efficiency, in miles per gallon HP Strength of the engine, in horsepower Repair Number of times the car was repaired before the auction Foreign Equals 1 if the car is foreign made, 0 otherwise

Multiple Regression Report

I need help with explaining the highlighted portions in the attached. I am trying to understand it as well as write an explanation before I do a research. Assumptions Address model assumptions. Begin by listing the assumptions and then presenting data or text that addresses how well the data meet the assumptions. For examp

Women's heights and pulse rates, linear correlation coefficient

A sample of 40 women is obtained and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.251 and the equation of the regression line is y=18.3 + 0.880x where x represents height. The mean of 40 heights is 62.8 in and the mean of the 40 pulse rates is 77.3 beats p

Simple Regression, Coefficient of Determination and Standard Error

A CEO of a large pharmaceutical company would like to determine if the company should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling diabetes. He wonders whether there is a strong relationship between the amount of money spent on television advertising for

Statistics and answer has to be in excel simple linear regression

Out-of-state tuition and fees at the top graduate schools of business can be very expensive, but the starting salary and bonus paid to graduates from many of these schools can be substantial. The following data show the out-of-state tuition and fees (rounded to the nearest $1000) and the average starting salary and bonus paid to

Multiple Regression Analysis Based on Minitab Output

Need assistance in interpreting the regression analysis to answer the question in the attached document. a. Analyze the Minitab output to determine the multiple regression equation. b. What conclusions are possible using the result of the global usefulness test (F test)? c. What conclusions are possible using the resu

Complete regression analysis using ACT score example

The focus sample contains information of the undergraduate students at the University of Wisconsin. Open Focus samples worksheet: a) Find the linear correlation coefficient between cumulative GPA and high school percentile for the 200 UWEC undergraduate students in the Focus sample b) Repeat part (a) for cumulative GPA and e

Measuring Stock Market Risk

I've attached an Excel file with the stock numbers. Please see my questions below. A) Can you help me determine which stocks are the most volatile? B) Help calculate the value of beta for each stock. I don't have a lot of experience with stock market performance but can you help me determine: C) Which of such stocks wo