Concept explainers
Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004) study of the accuracy of new software effort estimates, Exercise 12.114 (p. 757). Recall that stepwise regression was used to develop a model for the relative error in estimating effort (y) as a
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Statistics for Business and Economics (13th Edition)
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
- Assume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?arrow_forwardA logistic regression was used to investigate obesity and poor physical health while controlling for the following variables: age, gender, race, income, health status, education, current smoker, and diet/exercise status. Justify the use of a logistic regression.arrow_forwarda) Give a practical interpretation of the y-intercept of the regression line. b) What is the best-predicted value for the median hourly wage gain for the fifteenth year of schooling? c) The actual wage gain for the fifteenth year of schooling was 14%. How close was the predicted wage gain present to the actual value, i.e. what is the residual?arrow_forward
- If a scatterplot is created in excel, and a line of regression is fit along with a derived functional form, what does it mean to describe and interpret them? What conclusions would be made about relationships between two recorded variables?arrow_forwardThe owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x1) and newspaper advertising (*2). Weekly Gross Television Newspaper Revenue Advertising Advertising ($1000s) ($1000s) ($1000s) 96 6.0 2.5 90 2.0 3.0 96 5.0 2.5 92 3.5 2.5 96 4.0 3.3 95 3.5 3.3 94 2.5 4.2 95 4.0 3.5 The estimated regression equation was ŷ = 79.4 + 1.94x1 + 2.40x2. The computer solution provided SST = 33.5 and SSR = 29.283. a. Compute and interpret R2 and R. (to 3 decimals). R2 = R = b. When television advertising was the only independent variable, R = 0.653 and R = 0.595. Do you prefer the multiple regression results? Explain. No, because less variability is explained when both independent variables are usedarrow_forwardWe want to predict the percentage weight loss for 2011 participants, based on 2010 data. If we construct a simple linear regression model, predicting percentage weight loss as a function of starting weight, what are the values of y-intercept ("a") and regression coefficient ("b"), rounded to one and two decimal places?0.4 and 0.110.3 and 0.010.4 and 0.020.3 and 0.07According to the regression model calculated above, what is the value of "r", rounded to one decimal place?00.200.300.400.500.1 In the above question, what does "r" represent?Spearman's correlation coefficientPearson's correlation coefficientThe variability of the dependent variable explained by the independent variableThe variability of the independent variable explained by the dependent variable If we were to add "age" as an additional independent variable to the calculated regression model, we'd have a multiple linear regression equation. For such a model, would the calculated "R" be :- equal to or greater than the "r"…arrow_forward
- A major brokerage company has an office in Miami, Florida. The manager of the office is evaluated based on the number of new clients generated each quarter. Data were collected that show the number of new customers added during each quarter between 2015 and 2018. A multiple regression model was developed with the number of new customers as the dependent and the following four independent variables: Period (1, …, 16): A variable that measures the trend; Q1 = 1 for first quarter, Q1 = 0 otherwise; Q2 = 1 for second quarter, Q2 = 0 otherwise; Q3 = 1 for third quarter, Q3 = 0 otherwise. Questions: 1. Explain each of the four slopes (Period, Q1, Q2, Q3). 2. How many new customers would you expect in the second quarter of the following year (2019)?arrow_forwardThe owner of Showtime Movie Theaters, Inc., used multiple regression analysis to predict gross revenue (1) as a function of television advertising (Z1) and newspaper advertising (). Weekly Gross Television Newspaper Revenue Advertising Advertising ($1000s) ($1000s) ($1000s) 97 6.0 1.5 90 2.0 3.0 96 5.0 1.5 92 2.5 2.5 95 4.0 4.3 94 3.5 3.3 94 2.5 5.2 95 4.0 3.5 The estimated regression equation was y = 86.0 + 1.87z1 +0.71r2 The computer solution provided SST- 34.9 and SSR 32.700 a. Compute and interpret R and R: (to 3 decimals). R R b. When television advertising was the only independent variable, R = 0.653 and Ra = 0.595, Do you prefer the multiple regression results? Explain. Select your answer-arrow_forwardThe use of multiple logistic regression is warranted when there are two or more independent quantitative or nominal variables and one dichotomous dependent variable. a. True b. Falsearrow_forward
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