How does the association between age and math score change if gender is included in the analysis? Data AnalysesdaļANOVA RegressionExploration T-TestsLinear RegressionIDVerbal✓ Model BuilderPredictorsAgeGender↑88FrequenciesDependent VariableMathCovariatesAgeFactorsGenderBlocksBlock 1FactorGenderBlock 2Age+ Add New BlockXModel12jamovi - SAT FroDisModel ComparisonsComparisonModel1R0.04330.2275Model2InterceptGender:Omnibus ANOVA TestR²0.001870.05178AgeModel Specific Results Model 2AR²0.0499365GenderAge3328Residuals63242Note. Type 3 sum of squaresModel Coefficients - MathPredictorFemale - MaleSum of SquaresEstimate399.95F-8.637.250.03380.4641F0.895df1117SE146.1727.547.67Overall Model Testdf2df112df11Mean Square36533283720t2.736-0.3130.9461817df217F0.09810.8947Р0.0140.7580.357Р0.8560.636Р0.357Р0.7580.357[3]Stand. Estimate-0.1460.226 DataHOExploration T-Tests> Model BuilderAnalysesLinear RegressionFit MeasuresRR²Adjusted R²юн88ANOVA Regression Frequencies> Reference Levels> Assumption ChecksModel FitHOHючFactorsFactorOverall Model TestF test→→jamovi - SAT FroDisLinear RegressionModel Fit Measures1ModelRR²0.215 0.0463Omnibus ANOVA TestSum of SquaresAge3088Residuals63607Note. Type 3 sum of squaresModel Coefficients - MathPredictor EstimateIntercept 402.04Age6.92SE142.31dfF0.874118tOverall Model Testdf1df21Mean Square308835342.8257.40 0.935Р0.0110.36218F0.874P0.3620.215P0.362Stand. Estimate[3]

Linear Regression ID Verbal ✓ Model Builder Predictors Age Gender Dependent Variable Math Covariates Age Factors Gender Blocks Block 1 Gender Block 2 Age + Add New Block X X Model 1 2 Model Comparisons Comparison Model 1 R 0.0433 0.2275 Model -2 Omnibus ANOVA Test R² 0.00187 0.05178 Model Specific Results Model 2 Intercept Gender: Age AR² 0.0499 Gender Age Residuals Note. Type 3 sum of squares Sum of Squares Female - Male Model Coefficients - Math Predictor 365 3328 63242 F 0.0338 0.4641 -8.63 7.25 0.895 df 1 1 F 17 SE Estimate 399.95 146.17 27.54 7.67 Overall Model Test df1 df2 1 2 df1 1 Mean Square 365 3328 3720 t 18 17 -0.313 0.946 df2 17 F 0.0981 0.8947 P 2.736 0.014 0.758 0.357 Р 0.856 0.636 Р 0.357 Р 0.758 0.357 [3] Stand. Estimate -0.146 0.226

Linear Regression ID Verbal ✓ Model Builder Predictors Age Gender Dependent Variable Math Covariates Age Factors Gender Blocks Block 1 Gender Block 2 Age + Add New Block X X Model 1 2 Model Comparisons Comparison Model 1 R 0.0433 0.2275 Model -2 Omnibus ANOVA Test R² 0.00187 0.05178 Model Specific Results Model 2 Intercept Gender: Age AR² 0.0499 Gender Age Residuals Note. Type 3 sum of squares Sum of Squares Female - Male Model Coefficients - Math Predictor 365 3328 63242 F 0.0338 0.4641 -8.63 7.25 0.895 df 1 1 F 17 SE Estimate 399.95 146.17 27.54 7.67 Overall Model Test df1 df2 1 2 df1 1 Mean Square 365 3328 3720 t 18 17 -0.313 0.946 df2 17 F 0.0981 0.8947 P 2.736 0.014 0.758 0.357 Р 0.856 0.636 Р 0.357 Р 0.758 0.357 [3] Stand. Estimate -0.146 0.226

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 14CR

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2b) • Using a Graphing calculator or spreadsheet program, create the least squares regression line of the median student loan debt for graduates versus the average salary after 10 years. Be sure to define any variables. • Identify and interpret the correlation coefficient and coefficient of determination. • By looking at the scatterplot and the least squares regression line, determine the college that you believe is the best value. Explain your reasoning. • Using the college (Harvard University) you chose, identify and interpret its residual based on the least squares regression model.
Disk drives again In Chapter 6, Exercise 4, we saw somedata on hard drives. After correcting for an outlier, thesedata look like this: we want to predict Price from Capacity. Here is the regression analysis of Price vs. Capacity.Variable CoefficientIntercept 8.1006Num_Workers 0.9134Dependent variable is SalesR-squared = 93.2,s = 1.477 Dependent variable is PriceR-squared = 98.8,s = 17.95Variable CoefficientIntercept 18.617Capacity 103.929a) Write the regression equation. Define the variablesused in your equation.b) What does the slope mean in this context?c) What does the y-intercept mean in this context? Is itmeaningful?d) What would you predict for the price of a 3.0 TB drive?e) You found a 3.0 TB drive for $300. Is this a good buy?How much would you save compared to what youexpected to buy?f) Does the model overestimate or underestimate theprice for a 3.0 TB drive?
2a) • Using a Graphing calculator or spreadsheet program create a least squares regression line of the tuition for 4 years versus the average salary after 10 years, define any variables that you used. • Identify and interpret the correlation coefficient and coefficient of determination. • By looking at the least squares regression line, determine the college that you believe is the best value. Explain your reasoning. • Using the college (Harvard University) you chose, identify and interpret its residual based on the least squares regression model.
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Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained:The regression equation is *****PredictorCoef StDev t-ratio p-valueConstant1.7586 0.2525 6.9648 0.0000AGE 0.2124 0.3175 * 0.5042MIL -0.75270.3586 -2.0991 **ENG 4.8124 0.6196 7.7664 0.0000Analysis of VarianceSource DF SS MS F pRegression3 413.1291 138.7097*** 0.00Error 50 457.7607 2.2888Total 53a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, ‘***’and ‘***’. d) Hence…
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained: a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, and ‘***’. d) Hence test whether ? is significant. Give reasons for your answer. e) Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.
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A music critic was interested in whether particular variables measured on a song change over time. Two variables the critic considered were a song’s Tempo (in bpm) and a song’s Danceability. We will use the songs written before the year 2000 from the original SpotifySample data set. The data set that you will use to complete this investigation is called SpotifyB2000 and consists of 483 songs. Write the least-squares regression line equation describing Year and Danceability usingproper notation and values. Interpret the slope of the regression line for Year and Danceability in context. Would the interpretation of the y-intercept for Year and Danceability be meaningful? Ifso, interpret it. If not, state why not in one sentence. Calculate and record the coefficient of determination value r2for Year and Danceabilityand interpret this value in context. State the hypotheses for the test of the slope. Write the p-value found in the output from (n), and use the p-value provided in the…
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