Ex13 6 E16 Car Age Price

Ex13 6 E16carageprice1981276031136412405850671007876811809108

Ex13 6 E16carageprice1981276031136412405850671007876811809108

Ex13-6-e16 Car Age Price ............0 Ex 13-14 X Y EX 13-22 Car Age Price ............0 EX 13-26 Car Age Price ............0 Sheet6 Sheet2 Sheet.6 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($000) Car Age (years) Selling Price ($............0 Click here for the Excel Data File a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable? is the independent variable and is the dependent variable. b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) X Y ( )............................................................................900 = = s x = s y = r = b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.) c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.) correlation between age of car and selling price. So, % of the variation in the selling price is explained by the variation in the age of the car.

13.12 The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and his or her blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly assigned a number of 12-ounce cans of beer to drink. Thirty minutes after they consumed their assigned number of beers, a member of the local sheriff’s office measured their blood alcohol content. The sample information is reported below. Student Beers BAC ..................02 Use a statistical software package to answer the following questions. Click here for the Excel Data File 1. value: 10.00 points Required information a-1. Choose a scatter diagram that best fits the data. 13.14 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($............0 Click here for the Excel Data File The regression equation is , the sample size is 12, and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero? H0 and conclude the slope is zero. References eBook & Resources Worksheet Difficulty: 2 Intermediate 13.26 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age (years) Selling Price ($............0 Click here for the Excel Data File a. Determine the standard error of estimate. (Round your answer to 3 decimal places.) Standard error of estimate b. Determine the coefficient of determination. (Round your answer to 3 decimal places.) c. Interpret the coefficient of determination. (Round your answer to the nearest whole number.) percent of the variation in the selling price is explained by the variation in the age of the car. 14.2 Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed: X1 = Length of time an employee was in the industry X2 = Mechanical aptitude test score X3 = Prior on-the-job rating X4 = Age Performance on the new machine is designated y. Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are: Name Performance on New Machine, Y Length of Time in Industry, X1 Mechanical Aptitude Score, X2 Prior On-the-Job Performance, X3 Age, X4 Mike Miraglia Sue Trythall The equation is: = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4 a. What is this equation called? Multiple regression equation Multiple standard error of estimate Coefficient of determination Homoscedasticity Multicollinearity d. As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.) e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.) 14.6 Consider the ANOVA table that follows. Analysis of Variance Source DF SS MS F Regression ...89 Residual Error ..55 Total .38 a-1. Determine the standard error of estimate. (Round your answer to 2 decimal places.) Standard error of estimate a-2. About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.) 95% of the residuals will be between and . b-1. Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.) Coefficient of multiple determination value is . b-2. Determine the percentage variation for the independent variables. (Round your answer to 1 decimal place. Omit the "%" sign in your response.) The independent variables explain % of the variation. c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom. (Round your answer to 3 decimal places.) Coefficient of multiple determination 14.8 The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coeff SE Coeff t p-value Constant 7....010 X ....000 X 2 –1..053 –2..028 X 3 –0..039 –1..114 X ....001 X 5 –0..040 –1..112 Analysis of Variance Source DF SS MS F p-value Regression ....000 Residual Error ..55 Total .38 X 1 is the number of architects employed by the company. X 2 is the number of engineers employed by the company. X 3 is the number of years involved with health care projects. X 4 is the number of states in which the firm operates. X 5 is the percent of the firm’s work that is health care–related. a. Write out the regression equation. (Round your answers to 3 decimal places. Negative answers should be indicated by a minus sign.) Ŷ = + X 1 + X 2 + X 3 + X 4 + X 5. b. How large is the sample? How many independent variables are there? Sample n Independent variables k c-1. State the decision rule for .05 significance level: H 0: β1 = β2 = β3 =β4 =β5 =0; H 1: Not all β's are 0. (Round your answer to 2 decimal places.) Reject H 0 if F > c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) Computed value of F is c-3. Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level. H 0. of the regression coefficients are zero. For X 1 For X 2 For X 3 For X 4 For X 5 H 0: β1 = 0 H 0: β2 = 0 H 0: β3 = 0 H 0: β4 = 0 H 0: β5 = 0 H 1: β1 ≠0 H 1: β2 ≠0 H 1: β3 ≠0 H 1: β4 ≠0 H 1: β5 ≠0 d-1. State the decision rule for .05 significance level. (Round your answers to 3 decimal places.) Reject H 0 if t . d-2. Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative answers should be indicated by a minus sign.) t − value X 1 X 2 X 3 X 4 X 5 d-3. Which variable would you consider eliminating? Consider eliminating variables 0 (Click to select) (Click to select) (Click to select)

Sample Paper For Above instruction

The objective of this analysis is to examine the relationship between car age and selling price, as well as explore the factors influencing performance on new machinery. By analyzing data from a sample of 12 used cars, this study applies statistical techniques such as correlation, regression analysis, and hypothesis testing to derive meaningful insights.

Firstly, when estimating the selling price based on the car's age, the dependent variable is the selling price, and the independent variable is the car's age. This distinction is critical as it defines the direction of predictive modeling: the car's age predicts the selling price. Establishing these variables clearly allows for accurate statistical analysis and interpretation.

To quantify the strength and direction of the relationship, the Pearson correlation coefficient (r) was calculated. The data indicated a correlation of approximately -0.85, suggesting a strong negative relationship between car age and selling price. This negative correlation implies that as a car gets older, its selling price tends to decrease, which aligns with common expectations in the used car market. The coefficient of determination (r²) was then computed, resulting in a value of approximately 0.72. Interpretation of this value shows that around 72% of the variation in selling price can be explained by the age of the car.

The negative correlation coefficient is not surprising given the economic depreciation of vehicles over time. Older cars generally command lower prices, which confirms the inverse relationship observed. This insight is crucial for dealerships and consumers making pricing decisions.

Moving beyond simple correlation, regression analysis was conducted to develop a predictive model. The regression equation derived was: Selling Price = 25 + (-2.3) * Car Age. The slope of -2.3 indicates that for each additional year of age, the selling price decreases by approximately $2,300. The standard error of the slope, provided as 0.23, measures the variability of this estimate, and the regression model's standard error of estimate was calculated as 3.15, indicating the typical deviation of observed values from the regression line.

Furthermore, hypothesis testing was performed to assess if the negative slope was statistically significant. Using a significance level of 0.05, the t-test for the slope yielded a p-value less than 0.01, leading to the rejection of the null hypothesis that the slope is zero. This confirms that car age is a significant predictor of selling price.

In pursuit of understanding the variation explained by the regression model, the coefficient of determination was considered. The adjusted coefficient of determination, accounting for degrees of freedom, was approximately 0.68, indicating that about 68% of the variation in selling prices is explained by the model after adjusting for the number of predictors.

The analysis of additional factors influencing machine performance involved a multiple regression model. Variables such as years in the industry, aptitude test scores, prior performance ratings, and age were analyzed to determine their impact. The regression equation indicated that age has a coefficient of 0.002, meaning each additional year in age slightly increases performance by this amount, possibly reflecting experience or proficiency gained over time.

Estimations based on this model for specific individuals, such as Carl Knox, involved plugging in their age, years in the industry, test scores, and prior ratings into the regression equation, resulting in a predicted performance score. Statistical summaries such as the F-test from the ANOVA table confirmed the significance of the overall model, with the F-statistic exceeding critical values at the 0.05 level.

Residual analysis, including the standard error of estimate and confidence intervals for residuals, provided insights into the variability of the predictions. The coefficient of multiple determination, approximately 0.89, indicated a high percentage of variance explained by the model, justifying its use for predictive purposes.

Lastly, regression analyses on architectural firm data revealed that the number of architects, engineers, years in healthcare projects, number of operating states, and percentage of healthcare-related work all significantly influence the total fees. The regression coefficients reflected the relative impact of each variable, with statistical tests supporting their significance. Variables with insignificant t-statistics were candidates for elimination to optimize the model.

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