. The following sample observations were randomly selected.

X:53634468
Y:1315712131195

a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
. The following sample observations were randomly selected.

X:53634468
Y:1315712131195

a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
. The following sample observations were randomly selected.

X:53634468
Y:1315712131195

a. Determine the coefficient of correlation.
b. Determine the coefficient of determination.
c. Interpret the result.
XYXY

The 0.89 indicates a very strong negative relationship between X and Y.

b. The coefficient of determination is 0.7921, found by (0.89)2.

c. X accounts for 79 percent of the variation in Y.

2. Bi-lo Appliance Stores has outlets in several large metropolitan areas in New England. The general sales manager plans to air a commercial for a digital camera on selected local TV stations prior to a sale starting on Saturday and ending Sunday. She plans to get the information for Saturday-Sunday digital camera sales at the outlets and pair them with the number of times the advertisement was shown on the local TV stations. The purpose is to find whether there is any relationship between the number of times the advertisement was aired and digital camera sales. The pairings are: Location ofNumber ofSaturday-Sunday Sales

TV StationAirings($ thousands)

Providence415
Springfield28
New Haven521
Boston624
Hartford317
a. What is the dependent variable?
b. Draw a scatter diagram.
c. Determine the coefficient of correlation.
d. Determine the coefficient of...

...Economics 141 (Intro to Econometrics) Professor Yang
Spring 2001
Answers to Midterm Test No. 1
1. Consider a regression model of relating Y (the dependent variable) to X (the independent
variable) Yi = (0 + (1Xi+ (i where (i is the stochastic or error term. Suppose that the
estimated regression equation is stated as Yi = (0 + (1Xi and ei is the residual error term.
A. What is ei and define it precisely. Explain how it is related to (i.
ei is the residual error term in the sample regression function and is defined as eI hat = Y
– Y hat.
ei is the estimated error term of the population function.
B. What is (i and define it precisely. What are the four reasons for the inclusion of this error term in the population regression function (model)?
(i is the stochastic term in the population regression function. The four reasons for its existence are: 1. Omitted variable 2. Measurement error 3. Different functional form
4. to account for purely randomness in the human behavior.
C. Draw a graph where you can clearly show E(Yi(XI) = (( + ((XI and Yi = (0 + (1Xi. Show
also in your graph (( and e6 for the X6. This graph graph will show true and estimated
regression lines together with their respective error terms.
See Figure 2.1 on pages 18 (& 39) of the textbook for the graph.
D....

...LinearRegression 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 theregression 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...

...REGRESSION ANALYSIS
Correlation only indicates the degree and direction of relationship between two variables. It does not, necessarily connote a cause-effect relationship. Even when there are grounds to believe the causal relationship exits, correlation does not tell us which variable is the cause and which, the effect. For example, the demand for a commodity and its price will generally be found to be correlated, but the question whether demand depends on price or vice-versa; will not be answered by correlation.
The dictionary meaning of the ‘regression’ is the act of the returning or going back. The term ‘regression’ was first used by Francis Galton in 1877 while studying the relationship between the heights of fathers and sons.
“Regression is the measure of the average relationship between two or more variables in terms of the original units of data.”
The line of regression is the line, which gives the best estimate to the values of one variable for any specific values of other variables.
For two variables on regression analysis, there are two regression lines. One line as the regression of x on y and other is for regression of y on x.
These two regression line show the average relationship between the two variables. The regression line of y on x gives the most probable value of y for given value of...

...Simple LinearRegression 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 possiblelinear 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...

...SECTION A (You should attempt all 10 questions)
A1. Regression analysis is ____________________________________.
A) describes the strength of this linear relationship.
B) describes the mathematical relationship between two variables.
C) describes the pattern of the data.
D) describes the characteristic of independent variable.
A2. __________________ is used to illustrate any relationship between two variables.
A) Histogram
B) Pie chart
C) Scatter diagram
D) Frequency polygon
Questions A3 to A5 relate to the following information.
Suppose a firm fed the values of turnover, y, and advertising expenditure, x, (both in $000) for the past eight years, into a computer and obtained the regression relationship y = 26.7 + 8.5x.
A3. What is the dependent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A4. What is the independent variable?
A) Number of computers
B) Size of the firm
C) Turnover
D) Advertising expenditure
A5. If the advertising expenditure is $5000 in a particular year, estimate the turnover for that year.
A) $69,200
B) $42,526.70
C) $26.7
D) $69.20
A6. Explain what the following sample correlation coefficients tell you about the relationship between the x and y values in the sample:
r = - 0.8
A) No...

...the hedonic regression. This method is specific to breaking down items that are not homogenous commodities, to estimate value of its characteristics and ultimately determine a price based on the consumers’ willingness to pay. The approach in estimating the values is done by measuring the differences in the price of certain goods with regards to specific location. E.g. average cost of real estate is much lower in Missouri than in California. Location may be the biggest factor in real estate pricing.
2. Data and Regression Analysis
My data is for Blowing Rock, NC. It’s a resort town in the Blue Ridge Mountains. The attractions here are mostly outdoor activities taking place in the secluded wilderness. The population is only about 1500 and the average cost of a house from my data is $485,839.50.
For my linearregression, I am modeling the relationship between the price of homes, being my dependent variable, and some characteristics of the homes, being my explanatory variables. Originally my data consisted of the following for real estate in Blowing Rock, NC: price - selling price, miles from central business district, number of bedrooms, number of full bathrooms, number of half bathrooms, the year the home was built, square footage, number of garages, whether or not the house was located in a subdivision, lot size, if the house had a good view, number of days on the market, and difference between asking price...

...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...