The business question that I am addressing is whether the price (y-intercept) of a sample of used cars (n=50) has a relationship with the independent variables miles (k), mpg, year, and engine type. The best univariate technique to predict the value of (y) is the mean, which is $26, 268. The best technique to measure the y-intercept is how many miles (k) the used car has been driven by the previous owner. This was found by measuring the strongest correlation between price and the independent variables, its absolute value was thirty-eight percent. * The estimated equation is ŷ= 112.24x+32,162

The best way to interpret this equation is for every additional used car sold at $32,162 there is a decrease of 112k in y. 14.8% of the variation of the price can be explained by the equation. This was found by checking the r-squared, which is a powerful tool in Anova; it measures how well future outcomes are likely to be predicted by the model. The reason why we do hypothesis testing is; it’s an assertion about the distribution of one or more random variables. The hypothesis test can be set up:

H0: β1 = 0 With Alpha .05
Ha: Β1 ≠ 0
Reject H0, if p value is <.05
Do not reject Ha, if p value is > or equal to .05
The p value is .006
My decision: Is to reject H0, there is a significant relationship. The predicted model for the dependent variable I got by multiplying the first miles (k) into the equation ŷ= -112.24(100,000) +32,162 which gave me -11,191, 832. This means miles are predicted to decrease by 11,191,832 when price goes up by one. There is a strong negative relationship. The independent variables will affect price of used cars differently. The miles (k) of the car are going to increase/decrease the price of the car, if the miles on the car are too high (ex: over 120,000 miles; price $9,000 also depending on brand of car). The mpg (how many miles car travels on single gallon) is going to increase/decrease sales price of the car if...

...Regression Analysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multiple regressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10 different characteristics.
The test hypothesis that price is dependent on whether the car is convertible is superior to the other hypothesis tests conducted. The analysis performed showed that the test hypothesis with the smallest P-value was favorable, convertible cars had the smallest P-value.
The data that is used in this regression analysis to find the proper equation model for the relationship between price, age and mileage is from the Bryant/Smith Case 7 Tom’s Used Mustangs. As described in the case, the used car sales are determined largely by Tom’s gut feeling to determine his asking prices.
The most effective hypothesis test that exhibits a relationship with the mean price is if the car is convertible. The Regression Analysis is conducted to see if there is any relationship between the price and mileage, color, owner and age and GT. After running several models with different independent variables, it is concluded that there is a relationship between the price and...

...Simple Linear Regression in SPSS
1.
STAT 314
Ten Corvettes between 1 and 6 years old were randomly selected from last year’s sales records in Virginia Beach, Virginia. The following data were obtained, where x denotes age, in years, and y denotes sales price, in hundreds of dollars. x y a. b. c. d. e. f. g. h. i. j. k. l. m. 6 125 6 115 6 130 4 160 2 219 5 150 4 190 5 163 1 260 2 260
Graph the data in a scatterplot to determine if there is a possible linear relationship. Compute and interpret the linear correlation coefficient, r. Determine the regression equation for the data. Graph the regression equation and the data points. Identify outliers and potential influential observations. Compute and interpret the coefficient of determination, r2. Obtain the residuals and create a residual plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the variables in questions. At the 5% significance level, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is useful as a predictor of sales price for Corvettes? Obtain and interpret a 95% confidence interval for the slope, β, of the population regression line that relates age to sales price for Corvettes. Obtain a point estimate for the mean sales price of all 4-year-old Corvettes. Determine a 95% confidence...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly Auto Insurance Premium
5 2 12 9 15 6 25 16
$64 87 50 71 44 56 42 60
a. Does the insurance premium depend on the driving experience or does the driving experience depend on the insurance premium? Do you expect a positive or a negative relationship between these two variables? b. Compute SSxx, SSyy, and SSxy. c. Find the least squares regression line by choosing appropriate dependent and independent variables based on your answer in part a. d. Interpret the meaning of the values of a and b calculated in part c. e. Plot the scatter diagram and the regression line. f. Calculate r and r2 and explain what they mean. g. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. h. Compute the standard deviation of errors. i. Construct a 90% confidence interval for B. j. Test at the 5% significance level whether B is negative. k. Using α = .05, test whether ρ is different from zero.
Solution a. Based on theory and intuition, we...

...
MATH533: Applied Managerial Statistics
PROJECT PART C: Regression and Correlation Analysis
Using MINITAB perform the regression and correlation analysis for the data on SALES (Y) and CALLS (X), by answering the following questions:
1. Generate a scatterplot for SALES vs. CALLS, including the graph of the "best fit" line.
Interpret.
After interpreting the scatter plot, it is evident that the slope of the ‘best fit’ line is positive, which indicates that sales amount varies directly with calls. As call increases, the sales amount increases as well.
2. Determine the equation of the "best fit" line, which describes the relationship between
SALES and CALLS.
The equation of the ‘best fit’ line or the regression equation is SALES(Y) = 9.638 + 0.2018 CALLS(X1)
3. Determine the coefficient of correlation. Interpret:
MINTAB Results:
Correlations: SALES(Y), CALLS(X1)
Pearson correlation of SALES(Y) and CALLS(X1) = 0.871
P-Value = 0.000
The coefficient of correlation is 0.871. The correlation coefficient is positive so this indicates a positive or direct relationship between the variables. The correlation coefficient is far from the P-Value of 0.000. This means that there is an extremely low chance that Sales and Calls results are wrong and we can be confident in interpretation.
4. Determine the coefficient of determination. Interpret.
MINTAB Results:
S = 2.05708 R-Sq = 75.9% R-Sq(adj) =...

...Linear-Regression Analysis
Introduction
Whitner Autoplex located in Raytown, Missouri, is one of the AutoUSA dealerships. Whitner Autoplex includes Pontiac, GMC, and Buick franchises as well as a BMW store. Using data found on the AutoUSA website, Team D will use Linear Regression Analysis to determine whether the purchase price of a vehicle purchased from Whitner Autoplex increases as the age of the consumer purchasing the vehicle increases. The data set provided information about the purchasing price of 80 domestic and imported automobiles at Whitner Autoplex as well as the age of the consumers purchasing the vehicles. Team D selected the first 30 of the sampled domestic vehicles to use for this test. The business research question Team D will answer is: Does the purchase price of a consumer increase as the age of the consumer increases? Team D will use a linear-regression analysis to test the age of the consumers and the prices of the vehicles.
Five Step Hypothesis Testing
Team D will conduct the two-sample hypothesis using the following five steps:
1. Formulate the hypothesis
2. State the decision rule
3. Calculate the Test Statistic
4. Make the decision
5. Interpret the results
Step 1- Formulate the Hypothesis
Using the research question: Does the purchase price of an automobile purchased at Whitner Autoplex, increase as the age of the consumer purchasing the vehicle...

...The simple regression model (SRM) is model for association in the population between an explanatory variable X and response Y. The SRM states that these averages align on a line with intercept β0 and slope β1: µy|x = E(Y|X = x) = β0 + β1x
Deviation from the Mean
The deviation of observed responses around the conditional means µy|x are called errors (ε). The error’s equation: ε = y - µy|x
Errors can be positive or negative, depending on whether data lie above (positive) or below the conditional means (negative). Because the errors are not observed, the SRM makes three assumptions about them:
* Independent. The error for one observation is independent of the error for any other observation.
* Equal variance. All errors have the same variance, Var(ε) = σε2.
* Normal. The errors are normally distributed.
If these assumptions hold, then the collection of all possible errors forms a normal population with mean 0 and variance σε2, abbreviated ε ̴̴ N (0, σε2). Simple Regression Model (SRM) observed values of the response Y are linearly related to values of the explanatory variable X by the equation: y = β0 + β1x + ε, ε ̴̴ N (0, σε2)
The observations:
1. are independent of one another,
2. have equal variance σε2 around the regression line, and
3. are normally distributed around the regression line.
21.2 Conditions for the SRM ( Simple Regression Model )
Instead...

...STA9708
Regression Analysis: Literacy rates and Poverty rates
As we are aware, poverty rate serve as an indicator for a number of causes in the world. Poverty rates are linked with infant mortality, education, child labor and crime etc. In this project, I will apply the regression analysis learned in the Statistics course to study the relationship between literacy rates and poverty rates among different states in USA. In my study, the poverty rates will be the independent variable (x) and literacy rates will be the dependent variable (y). The purpose of this regression is to determine if there is a correlation between the poverty rates and literacy rates in different states within USA. My null and alternate hypothesis are as follows:
Null hypothesis: Ho: β1 = 0 This hypothesis states that there is no correlation between the literacy and poverty rates
Alternate hypothesis: Ha: β1≠0 This is the hypothesis we want to prove, there is correlation between the literacy rate and poverty rates
The first step I did was to create a scatter plot for the data and the descriptive statistics study. The scatter plot shows a positive correlation between the two variables and the equation of the line is y = 1.0998x + 2.2613 with a R-square value of 0.5305. The scatter plot is shown below:
Figure 1: Scatter plot of relationship between poverty and literacy rates
Based on the coefficient of determination of 0.53, we can say that poverty...

...Managerial Economics
Regression Analysis Report
23rd Feb 2015
Instructor: Professor Larry Haverkamp
Submitted by
(Group 4)
Bhadrinath Ramachandran
Yang Yachieh (Missy)
Stuti Kumar
KEE Cheng Huat (Richard)
WOO Sou Khuen (Jun)
Table of Contents
1.0 Introduction……………………………………………………………………………….3
1.1 Regression Analysis – Our Approach……………………………………………………..3
1.2 Cross-Section Regression Analysis……………………………………………………….3
1.2.1 Factors that could affect the Divorce Rates (Hypothesis)………………………...4
1.2.2 Data Collection……………………………………………………………………4
1.2.3 Results and Conclusion……………………………………………………………5
1.3 Time-series Regression Analysis………………………………………………………….6
1.3.1 Factors that could affect the fertility rate………………………………………….6
1.3.2 Data Collection……………………………………………………………………6
1.3.3 Regression Analysis……………………………………………………………….6
1.3.4 Prediction...………………………………………………………………………10
1.0 Introduction
This report is written to study two different approaches to regression analysis, namely the cross-sectional regression and the time-series regression. The study of cross-sectional regression is conducted using the data of divorce to marriage...