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Words 1184

Pages 5

TUTORIAL CHAPTER 3 – INTRODUCTORY LINEAR REGRESSION

1) Given 5 observations for two variables, x and y.

| 3 | 12 | 6 | 20 | 14 |

| 55 | 40 | 55 | 10 | 15 |

a. Develop a scatter diagram for these data.

b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

c. Develop the estimated regression equation by computing the values and.

d. Use the estimated regression equation to predict the value of y when x=10.

e. Compute the coefficient of determination. Comment on the goodness of fit.

f. Compute the sample correlation coefficient (r) and explain the result.

2) The Tenaga Elektik MN Company is studying the relationship between kilowatt-hours (thousands) used and the number of room in a private single-family residence. A random sample of 10 homes yielded the following.

Number of rooms | Kilowatt-Hours (thousands) |

12 9 14 6 10 8 10 10 5 7 | 9 7 10 5 8 6 8 10 4 7 |

a. Identify the independent and dependent variable.

b. Compute the coefficient of correlation and explain.

c. Compute the coefficient of determination and explain.

d. Test whether there is a positive correlation between both variables. Use α=0.05.

e. Determine the regression equation (used Least Square method)

f. Determine the value of kilowatt-hours used if number of rooms is 11.

g. Can you use the model in (f.) to predict the kilowatt-hours if number of rooms is 20? Explain your answer.

3) Mr Rama, president of Dan Din Dun Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr Rama gathered the following sample information. The X indicates the number of client contacts last month, and the Y shows the value of sales (RM thousands) last month…...

...Introduction Regression analysis was developed by Francis Galton in 1886 to determine the weight of mother/daughter sweet peas. Regression analysis is a parametric test used for the inference from a sample to a population. The goal of regression analysis is to investigate how effective one or more variables are in predicting the value of a dependent variable. In the following we conduct three simple regression analyses. Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.616038 R Square 0.379503 Adjusted R Square 0.371338 Standard Error 0.773609 Observations 78 ANOVA df SS MS F Significance F Regression 1 27.81836 27.81836 46.48237 1.93E-09 Residual 76 45.48382 0.598471 Total 77 73.30218 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.897327 0.310671 9.326021 3.18E-14 2.278571 3.516082 2.278571 3.516082 X Variable 1 0.42507 0.062347 6.817798 1.93E-09 0.300895 0.549245 0.300895 0.549245 Graph Benefits and Extrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.516369 R Square 0.266637 Adjusted R Square 0.256987 Standard Error 0.35314 Observations 78 ANOVA...

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...Ben Leigh American Intercontinental University Unit 5 Individual Project BUSN311-1301B-10: Quantitative Methods and Analysis Instructor Leonidas Murembya April 23, 2013, Abstract This paper will be discussing regression analysis using AIU’s survey responses from the AIU data set in order to complete a regression analysis for benefits & intrinsic, benefits & extrinsic and benefit and overall job satisfaction. Plus giving an overview of these regressions along with what it would mean to a manager (AIU Online). Introduction Regression analysis can help us predict how the needs of a company are changing and where the greatest need will be. That allows companies to hire employees they need before they are needed so they are not caught in a lurch. Our regression analysis looks at comparing two factors only, an independent variable and dependent variable (Murembya, 2013). Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.018314784 R Square 0.000335431 The portion of the relations explained Adjusted R Square -0.009865228 by the line 0.00033% of relation is Standard Error 1.197079687 Linear. Observations 100 ANOVA df SS MS F Significance F Regression 1 0.04712176 0.047122 0.032883 0.856477174 Residual 98 140.4339782 1.433 Total 99 140.4811 Coefficients Standard Error t...

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...Q1: All the regressions were performed. Output can be made available if needed. See outputs for Q2 in appendix. Q2: Select the model you are going to keep for each brand and explain WHY. Report the corresponding output in an appendix attached to your report (hence, 1 output per brand) We use Adjusted R Squared to compare the Linear or Semilog Regression. R^2 is a statistic that will give some information about the goodness of fit of a model. In regression, the Adjusted R^2 coefficient of determination is a statistical measure of how well the regression line approximates the real data points. An R2 of 1 indicates that the regression line perfectly fits the data. Brand1: Linear Regression R^2 | 0.594 | SemiLog Regression R^2 | 0.563 | We use the Linear Regression Model since R-squared is higher. Brand 2: Linear Regression R^2 | 0.758 | SemiLog Regression R^2 | 0.588 | We use the Linear Regression Model since R-squared is higher Brand 3: Linear Regression R^2 | 0.352 | SemiLog Regression R^2 | 0.571 | We use the Semilog Regression Model since R-squared is higher Brand 4: Linear Regression R^2 | 0.864 | SemiLog Regression R^2 | 0.603 | We use the Linear Regression Model since R-squared is higher Q3: Here we compute the cross-price elasticity. Depending on whether we use linear or semi-log model, Linear Model Linear Model Semi-Log Model Semi-Log Model...

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...Introduction The flowing charts are to show if there is any relationships between the variables. The relationships can either be negative or positive. This is told by whether the graph increases or decreases. Benefits and Intrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.069642247 R Square 0.004850043 Adjusted R Square -0.00471871 Standard Error 0.893876875 Observations 106 ANOVA df SS MS F Significance F Regression 1 0.404991362 0.404991 0.50686 0.478094147 Residual 104 83.09765015 0.799016 Total 105 83.50264151 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.506191723 0.363736853 15.13784 4.8E-28 4.784887893 6.2274956 4.7848879 6.22749555 Benefits -0.05716561 0.080295211 -0.711943 0.47809 -0.21639402 0.1020628 -0.216394 0.10206281 Y=5.5062+-0.0572x Graph Benefits and Extrinsic Job Satisfaction Regression output from Excel SUMMARY OUTPUT Regression Statistics Multiple R 0.161906 R Square 0.026214 Adjusted R Square 0.01685 Standard Error 1.001305 Observations 106 ANOVA df SS MS F Significance F Regression 1 2.806919 2.806919 2.799606 0.097293 Residual 104 104.2717 1.002612 Total 105 107.0786...

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...Linear Regression deals with the numerical measures to express the relationship between two variables. Relationships between variables can either be strong or weak or even direct or inverse. A few examples may be the amount McDonald’s spends on advertising per month and the amount of total sales in a month. Additionally the amount of study time one puts toward this statistics in comparison to the grades they receive may be analyzed using the regression method. The formal definition of Regression Analysis is the equation that allows one to estimate the value of one variable based on the value of another. Key objectives in performing a regression analysis include estimating the dependent variable Y based on a selected value of the independent variable X. To explain, Nike could possibly measurer how much they spend on celebrity endorsements and the affect it has on sales in a month. When measuring, the amount spent celebrity endorsements would be the independent X variable. Without the X variable, Y would be impossible to estimate. The general from of the regression equation is Y hat "=a + bX" where Y hat is the estimated value of the estimated value of the Y variable for a selected X value. a represents the Y-Intercept, therefore, it is the estimated value of Y when X=0. Furthermore, b is the slope of the line or the average change in Y hat for each change of one unit in the independent variable X. Finally, X is any value of the independent variable that is selected...

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...STATISTICS FOR ENGINEERS (EQT 373) TUTORIAL CHAPTER 3 – INTRODUCTORY LINEAR REGRESSION 1) Given 5 observations for two variables, x and y. | 3 | 12 | 6 | 20 | 14 | | 55 | 40 | 55 | 10 | 15 | a. Develop a scatter diagram for these data. b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Develop the estimated regression equation by computing the values and. d. Use the estimated regression equation to predict the value of y when x=10. e. Compute the coefficient of determination. Comment on the goodness of fit. f. Compute the sample correlation coefficient (r) and explain the result. 2) The Tenaga Elektik MN Company is studying the relationship between kilowatt-hours (thousands) used and the number of room in a private single-family residence. A random sample of 10 homes yielded the following. Number of rooms | Kilowatt-Hours (thousands) | 12 9 14 6 10 8 10 10 5 7 | 9 7 10 5 8 6 8 10 4 7 | a. Identify the independent and dependent variable. b. Compute the coefficient of correlation and explain. c. Compute the coefficient of determination and explain. d. Test whether there is a positive correlation between both variables. Use α=0.05. e. Determine the regression equation (used Least Square method) f. Determine the value of kilowatt-hours used if number of rooms is 11. g. Can you use the model in (f.) to predict the kilowatt-hours if number of...

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...Acts 430 Regression Analysis In this project, we are required to forecast number of houses sold in the United States by creating a regression analysis using the SAS program. We initially find out the dependent variable which known as HSN1F. 30-yr conventional Mortgage rate, real import of good and money stock, these three different kinds of data we considered as independent variables, which can be seen as the factors will impact the market of house sold in USA. Intuitively, we thought 30-yr conventional mortgage rate is a significant factor that will influences our behavior in house sold market, which has a negative relation with number of house sold. When mortgage rate increases, which means people are paying relatively more to buy a house, which will leads to a decrease tendency in house sold market. By contrast, a lower interest rate would impulse the market. We believe that real import good and service is another factor that will causes up and down in house sold market. When a large amount of goods and services imported by a country, that means we give out a lot of money to other country. In other words, people have less money, the sales of houses decreased. Otherwise, less import of goods and services indicates an increase tendency in house sold market. We can see it also has a negative relationship with the number of house sold. Lastly, we have money stock as our third impact factor of house sold. We considered it has a positive relationship with the number...

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...Applied Regression Analysis 41100-81 Christian Hansen Winter 2015 “I pledge my honor that I have not violated the Honor Code during this assignment.” Kataras, Peter Foltyn, Tom Erzen, Robert Scholl, Katie In order to begin we first had to gain a high level understanding of the 6000 observations that we were given. We ran descriptive statistics on all of the original variables after transforming the variable Color into a dummy variable called White (White Wine=1, Red wine=0). Descriptive Statistics | | N | Minimum | Maximum | Mean | Std. Deviation | quality | 6000 | 2.5000 | 9.5000 | 5.825317 | .9206965 | fixed_acidity | 6000 | 3.8000 | 15.9000 | 7.221233 | 1.3094165 | volatile_acidity | 6000 | .0800 | 1.5800 | .340727 | .1653986 | citric_acid | 6000 | .0000 | 1.6600 | .318008 | .1455540 | residual_sugar | 6000 | .6000 | 65.8000 | 5.425650 | 4.7411670 | chlorides | 6000 | .0100 | .6100 | .056483 | .0344872 | free_sulfur_dioxide | 6000 | 1.0 | 289.0 | 30.482 | 17.7550 | total_sulfur_dioxide | 6000 | 6.0 | 440.0 | 115.576 | 56.5940 | density | 6000 | .99 | 1.04 | .9949 | .00504 | pH | 6000 | 2.74 | 4.01 | 3.2195 | .16022 | sulphates | 6000 | .2200 | 2.0000 | .532073 | .1487300 | alcohol | 6000 | 8.0000 | 14.9000 | 10.491008 | 1.1901957 | White | 6000 | 0 | 1 | .75 | .433 | Some of our variables in the dataset have very tight ranges, for example density has a min of .99 and a max of 1.04. On the other hand, total sulfur...

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...Regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Local Government Engineering Department (LGED) is a public sector organization under the ministry of Local Government, Rural Development & Cooperatives. The prime mandate of LGED is to plan, develop and maintain local level rural, urban and small scale water resources infrastructure throughout the country. Here, I considered LGED as the organization and considering a projects eight districts “available fund” as Independent variable and “development (length of development of road in km)” as dependent variable. The value of the variables are- Districts Fund, X (lakh tk) Development,Y (km) Panchagar 450 10 Thakurgaon 310 6.8 Dinajpur 1500 32 Nilphamari 1160 24.5 Rangpur 1450 31 Kurigram 450 9 Lalmonirhat 950 16 Gaibandha 1550 33 For the two variables “available fund” and “development”, the regression equation can be given as: Y= a + bX Where, Y = Development X = Fund b = rate of change of development...

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...Regression Paper Introduction The purpose of regression analysis is to find out the values of parameters for a purpose that cause the purpose to best fit a set of selected data observations. The description of this linear regression test will be explained and analyzed in the paper. The data collected for various teams will help comparing the numbers with the anticipation of getting a reliable and comparable hypothesis test answer. Having enough data will give the test a fare chance to show the results needed for a positive outcome. Conclusion In finishing the regression analyses, team D can conclude that there seems to be a linear relationship between the salary affect of the performance players based on the win and losses. Team D formulated both verbal and numerical hypothesis statements on the salaries of Major League Baseball players. In addition to using the regression hypothesis test linear, the Team also studies the data given by the Major League Baseball player’s data. This analysis confirms that the mean salary for Major League Baseball players is considerably correlated to the team wins. The sample mean of team salaries and the sample mean of wins of our data set are prime variables. Using regression analysis played an important role in helping us answer the research question of if the salary of Major League Baseball players is connected to the wins of Major League Baseball teams. Reference Doane, D., & Seward, L. (2007). Applied Statistics in......

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... Case Study: Locating New Pam and Susan‘s Stores Professor Demetra Paparounas Lisa Chan MGSC 6200- Information Analysis July 3, 2014 Introduction The purpose of this study to is to determine a new store location for Pam and Susan Stores. This discount department store chain has 250 stores that are primarily in the South. Expansion is important to their strategic success. A multiple regression model will be used to determine which location has the highest sales potential and projections. It will also be used to help see how strong of a relationship sales has to the other independent variables. Data For this model, the wealth of census data that was used to compute this model contained 250 observations, 33 variables and 7 additional dummy variables were created from the main comtype variable, taking values of zero or one depending on level of competitiveness for a particular store. This data set contained economic and demographical data, population type, sales numbers, store size and the competitive types. The amount of sales and selling square feet variables are given in thousands of dollars. Results and Discussions In analyzing the data on the 250 Pam and Susan’s stores, we first created a scatter plot of the competitive types in the horizontal axis against sales (in thousands) on the vertical axis. The competitive types were identified as follows: * Type 1- Densely populated area with relatively little direct competition. * Type 2 –High income areas with little...

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...ANALYSIS OF REGRESSION Jessica Cain American InterContinental University Abstract The world today uses statistics in many different ways to understand numbers and possible outcomes. One way that this is by using regression analysis. The regression analysis which is based on a correlation between two variables can help us to better understand the relationship between the two variables. The process which is a valuable one has helped researchers, and businesses to grow based on information obtained from a regression analysis that contains a linear regression. Introduction The purpose of a regression analysis is to help show a linear regression of certain variables. This helps to understand the correlation of the variables being tested. Correlation does give reason to suspect that the relationship between two variables is not die to chance or other hidden variables (Editorial Board, [EB], 2012). This is done by utilizing excel to show how the variables match up, and if one is causing the other or if there are outliers that are affecting the outcome. This is important as it will allow for a company to see and eliminate these unnecessary variables and continue their growth. Benefits and Intrinsic Job Satisfaction Regression output from Excel |SUMMARY OUTPUT | | | | | |Intrinsic |-0.08484 |4.844477 |Y...

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...A) Estimated regression equation – First Order: y = β0 + β1x1 + β2x2 + ε Output of 1st Model | | | | | | | | | | | | | | Regression Statistics | | | | | | Multiple R | 0.763064634 | | | | | | R Square | 0.582267636 | SSR/SST | | ̂̂̂ | | | Adjusted R Square | 0.512645575 | | | | | | Standard Error | 547.737482 | | | | | | Observations | 15 | | | | | | | | | | | | | ANOVA | | | | | | | | df | SS | MS | F | Significance F | | Regression | 2 | 5018231.543 | 2509115.772 | 8.363263464 | 0.005313599 | | Residual | 12 | 3600196.19 | 300016.3492 | | | | Total | 14 | 8618427.733 | | | | | | | | | | | | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Intercept | -20.35201243 | 652.7453202 | -0.031179101 | 0.975639286 | -1442.561891 | 1401.857866 | Age (x1) | 13.35044655 | 7.671676501 | 1.740225432 | 0.107375657 | -3.364700634 | 30.06559374 | Hours (x2) | 243.7144645 | 63.51173661 | 3.837313819 | 0.002363965 | 105.334278 | 382.0946511 | B) equation | ŷ= -20.3520124320994 + 13.3504465516772 x̂1 + 243.714464532425 x̂2 | C) Interpretation of β β̂1 = 13.35044655, If number of hours worked (x2) held fixed, we can estimate that every one-year increase in age (x1) the mean of annual earnings will increase by 13.35044655. β̂2 = 243.7144645, If age (X1) held fixed, we can estimate that every one hour (x2) of work increase, the mean of...

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...------------------------------------------------- REYEM AFFAIR Regression Case Quantitative Methods II To ------------------------------------------------- Prof. Arnab Basu On October 21, 2011 By GROUP NO. 5 Bharati vishal (11110) akshay ram (11110) dhanashree vinayak shirodkar (11110) amol devnath kumbhare (11110) ajusal sugathan (11110) arun prabu (11110) ghule nilesh vishnu (11110) mudavath swetha (11110) Raja Simon J (1111052) sagar behera (11110) shreya sethi (11110) swati murarka (11110) Indian Institute Of Management, Bangalore Table of Contents S.No | Particulars | Pages | 1. | Executive Summary | 3-4 | 2. | Understanding of the Problem | 4 | 3. | Model Description | 5-13 | | Model 1Prediction interval Vs Confidence IntervalStep wise Regression: A closer lookTest of Model: Analysis of Results | 5-8 | | | 6 | | | 7 | | | 8 | | Model 2Test of Model: Analysis of Results | 9-13 | | | 11-13 | | Other Models | 13 | 4. | Conclusions and Recommendations | 14 | 5. | Appendix 1. Variables Entered/Removed 2. Model Summary 3. ANOVA 4. Coefficients 5. Residual Statistics | 15 | Executive Summary Reyem Affiar has recently found the below described condominium in Mid-Cambridge that he wants to purchase. Street Address : 236 Ellery Street Last Price : $169000 Area & Area Code : M/9 Bed : 2 Bath : 1 Rooms : 5 Interior : 1040 Condo : $175 Tax : $1121 RC : 1...

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...Unit 5 – Regression Analysis Jessica Laux/Bakos American InterContinental University Abstract Data regression and charting are important parts of interpreting data. If one uses scatter plots, and data analysis, one can determine if a correlation exists between two data sets, or if there is actually very little. This can help when it comes to seeing for example, if job satisfaction overall is related to benefits, and if so how to change that in the favor of the business. Introduction In the following information, we will show regression outputs for data sets from the AIU data set. We will determine correlation and what it means, as well as show scatter graphs that can help determine if there is any correlation to be shown. One has to be careful to input the proper data if they want the analysis to come out correctly. Benefits and Intrinsic Job Satisfaction Regression output from Excel |SUMMARY OUTPUT | | | | | |Intrinsic |0.326704508 |3.438142011 |Y=0.0034x+4.5491 |0.0012 | |Extrinsic |-0.134516538 |6.034361553 |Y=1.6912x+13.859 |0.2275 | |Overall |0.101037811 |4.712869316 |Y=1.0105x+0.5195 |0.1021 | Similarities and...

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