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Coefficient of Determination

The coefficient of determination indicates how well data points fit a line or curve. It is denoted by R2 and pronounced R squared. It is a statistic used in the context of statistical models whose main purpose is either to prediction of future outcomes or the testing of hypotheses on the basis of other related information. It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. The coefficient of determination provides a measure of how well observed outcomes are replicated by the model as the proportion of total variation of outcomes explained by the model.

There are many definitions of R2 which are only sometimes equivalent; for example linear regression. If an intercept is included then R2 is simply the square of the sample correlation coefficient between the outcome and their predicted values. If an intercept is included and the number of explanators is more than one, R2 is the square of the coefficient of multiple correlations. In these cases, the coefficient of determination ranges from 0 to 1.

R2 is a statistic that will give some information about the goodness of fit of a model. In regression, the R2 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. However, the R2 value can range outside 0 to 1 where it is used to measure the agreement between observed and modeled values, where the modeled values are not obtained by linear regression. 

Simple and Multiple Linear Regression Calculations

See the attached file. 1. Use the following results obtained from a simple linear regression analysis with 15 observations. Y ̂ = 35.5- (1.75)X R2= 0.9345 and sb1 = 0.60 Interpret regression results and the value of the coefficient of Determination. Predict the value of Y when X is equal to 10. Calculated the correl

Geometry: Length and Perimeter

1. If the hypotenuse of a right triangle is 5 m more than the longer leg, and the shorter leg is 15 m long, find the length of the longer leg. The longer leg is____m. 2. The perimeter P of the rectabgle equals 218. Find the value of x. (left side of rectangle 2x-3) (Base of rectangle 3x+7). x=? 3. Suppose a carpet for a 6

Chi Square Analysis of Clothing Case Study

A survey of 1,085 adults asked, "Do you enjoy shopping for clothing for yourself?" The results indicated that 51% of the females enjoyed shopping for clothing for themselves as compared to 44% of the males. (Data extracted from "Split Decision on Clothes Shopping," USA Today, January 28, 2011, p. 1B.) The sample sizes of males a

Performing a Complete Regression Analysis using Given Data

An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 20 metal sheets are given below. Use the simple linear regression model. ∑X = 40 ∑X2 = 200 ∑Y = 70 ∑Y2 = 545 ∑XY = 300 Find the estimated y intercept and slope and write the eq

Interpretation of Correlation Coefficient, Slope and Scatter Plot

Assess the relationship between the two variables based on the scatterplot and output for the b coefficient. Is there a relationship between these two variables as hypothesized? Is it a negative or a positive relationship? Describe the relationship between these two variables using representative values of years of education

Statistical Concepts Clarification

I need some help in providing short clarifications on these points: 1. Is IQ test scores considered interval scale? 2. What type of research design is the strongest when I what to adopt a new educational program? Using a pre-test and post-test with control group, the previous method but without the control group, or comparing

Calculating Coefficient of Determination and Standard Error of Estimate

See the attached file. The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is y = 0.956x + 15.099. Complete parts a and b. Money raised, x Money spent, y 462.4 443.4 674.3 678.2 744.2 749.7 776.2

Coefficeint of Correlation and Coefficient of Determination

In a study of a 130 female college undergraduates and their parents, each triad of daughter, mother and father completed the UCLA loneliness scale. a. The correlation between daughter's loneliness score y and mother's loneliness score x was determined to be r = 0.26. b. The correlation between daughter's loneliness score y and

Coefficient of Correlation & Determination

(15.42) For each of 10 popular prescription drugs, file XR15042 lists the retrail price (in U.S. dollars) for the drug in secveral different countries, including the United States, Canada, Great Britain, and Australia. Determine and interpret the coefficients of correlation and determination for U. S. prices versus Canadian p

Variables: coefficient of determination, coefficient of correlation

The following information regarding a dependent variable Y and an independent variable X is provided. EX = 16 E (X - X)(Y - Y) = -8 EY = 28 E (X - X)2 = 8 n = 4 SST = 42 SSE = 34 The coefficient of determination is A. 0.1905 B. -0.1905 C. 0.4364 D. -0.4364 The coefficient of correlatio

Statistical analysis: Coefficient of correlation; coefficient of determination

See attached file. There a 3 problems. Please follow instructions on document which includes showing all work. Do not include attachments. Note below the point value of each exercise. Show all calculations for credit. A. Use Excel or Megastat to determine the following correlations of analysis: X 2 3 5 5 10 y 6 9 1

Coefficient of determination

The test scores of 6 randomly picked students and the numbers of hours they prepared are as follows: Hours: 5 10 4 6 10 9 Score: 64 86 69 86 59 87 The equation of the regression line is y(^on top)=1.06604x+67.3491. Find the coefficient of determination.

Statistics - Coefficient of Determination

Finding variations and the coefficient of determination Use the data to find the (a) coefficient of determination and interpret the result, and (b) standard error of estimate Se and interpret the result. Earnings of Men and women. The table shows median weekly earnings (in U.S. dollars) of full-time male and female workers fo

Regression Analysis and Coefficient of Determination

A metropolitan economist is attempting to predict the average total budget of retired couples in Phoenix, based on average U.S. urban retired couples' total budget. An r2 of .7824 is obtained. Will the regression be a good predictive model?

SST, SSE, SSR, Coefficient of Determination, & Goodness of Fit

Can you please show me calculations as how to obtain the answer? The following data represent the number of weed-eaters sold per month at a local garden shop and their prices Price x $34 36 32 35 30 38 40 Units sold y 3 4 6 5 9 2 1 a. Compute SST, SS

Data analysis: scatter plot, coefficient of correlation and more

A major oil company is studying the relationship between the daily traffic count and the number of gallons of gasoline pumped at company stations. A sample of eight company owned stations is selected and the following information obtained: a) develop a scatter diagram with the amount of gasoline pumped as the dependent variab

Calculating Coefficient of Determination

In a regression analysis, the sum of the squared deviations between y and y-bar is SST = 200.0. If the sum of the squared deviations about the regression line is SSE + 40.0, what is the coefficient of determination?

Calculating the Coefficient of Determination

The following results were obtained from a simple linear regression analysis. Total sum of square = 5.7640. Explained sum of squares = 5.5415. Unexplained sum of squares = 0.2225. The coefficient of determination is ____

The Coefficient of Correlation and of Determination

Question: The correlation coefficient for a relation is y = 0.5. Find the coefficient of determination (round to nearest hundredth). Find the percentage of the total variation that can be explained by the linear relationship between the two variables (round to the nearest whole percent).

Coefficient of Correlation and Determination

1. The following sample observations were randomly selected. x 4 5 3 6 10 y 4 6 5 7 7 Determine the coefficient of correlation and the coefficient of determination. Interpret. 2. The following sample observations were randomly selected. x 5 3 6 3 4 4 6 6 y 13 15 7 12 13 11

Coefficient of Correlation, Determination, & Test

What is the relationship between the amount spent per week on food and the size of the family? Do larger families spend more on food? A sample of 10 families in the Chicago area revealed the following figures for family size and the amount spent of food per week. Family Size Amount Spent 3 $99 6 $104 5 $151 6 $129 6

Correlation, Coefficient of Determination

1. Given the following N's (where N is the number of pairs of observations) and obtained r's, indicate whether the result is significant at the .05 level: (a) N = 100, r = .22 (b) N = 100, r = .60 (c) N = 9, r = -.70 (d) N = 36, r = .23 (e) N = 100, r = -.19 2. Given the following data, what are the correlation and t