a. Does the intercept have a useful interpretation in this study? Why or why not.b. Interpret the effect of a unit increase in Length on the response of Weight 1. A study was conducted to investigate the relationship between an alligator's weight (in pounds) and its snout length (in inches). The response variable is the alligator’s weight, and we want to study if the covariate of snout length helps explain the response.Data is collected on 14 alligators, and the linear regression output from R is below. ### Regression Analysis Summary#### Residuals:``` Min 1Q Median 3Q Max-0.24348 -0.03186 0.03740 0.07727 0.12669```#### Coefficients:| | Estimate | Std. Error | t value | Pr(>|t|) ||---------------|-----------|------------|---------|----------|| (Intercept) | -8.4761 | 0.5007 | -16.93 | 3.08e-10 *** || Length | 13.7244 | 0.5320 | 25.80 | 1.49e-12 *** |#### Statistical Measures:- **Residual standard error:** 0.1229 on 13 degrees of freedom- **Multiple R-squared:** 0.9808 - **Adjusted R-squared:** 0.9794- **F-statistic:** 665.8 on 1 and 13 DF, **p-value:** 1.495e-12### Explanation:1. **Residuals** section: - Displays the summary statistics (Min, 1Q, Median, 3Q, Max) for residuals, which are the differences between observed and predicted values.2. **Coefficients** section: - Provides estimates for the regression coefficients, standard errors, t-values, and p-values. `Estimate` represents the estimated effect of each predictor. A high t-value and low p-value (Pr(>|t|) less than 0.05) suggests that the predictors are statistically significant. - The significance codes `***` indicate that the coefficients are significant well below typical thresholds (0.001).3. **Statistical Measures**: - **Residual standard error:** Measures the average amount by which the response variable deviates from the predicted value. - **Multiple R-squared**: Proportion of the variance in the dependent variable that is predictable from the independent variable(s). - **Adjusted R-squared**: Adjusted version of R-squared that has been adjusted for the number of predictors in the model. - **F-statistic**: Used to test the overall significance of the model. A large F-statistic and a small p-value indicate a significant regression model.

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MATLAB: An Introduction with Applications

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Chapter1: Starting With Matlab

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Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T P Constant -0.212 2.429 -0.09 0.929 Diameter 0.7527 0.1686 5.33 0.013 S = 4.16190 R-Sq = 81.2% (c) The formula for the margin of error E for a c% confidence interval for the slope ? can be written as E = tc(SE Coef). The Minitab display is based on n = 12 data pairs. Find the critical value tc for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope ?. (Use 3 decimal places.) tc lower limit upper…
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Here are the world record race times for women in the 10,000-meter run over several years. a) Which is the explanatory variable and which is the response variable? Year Race Time (seconds) 1967 2286.4 b) Make a scatterplot of these data. You do not have to draw the scatterplot for me. Describe what you see (form, direction, 1970 2130.5 1975 2100.4 strength, outliers). 1975 2041.4 c) Write the equation of the regression line for predicting race time from year. 1977 1995.1 1979 1972.5 d) Give the meaning of the slope of your line in terms of race time and year. What are the units of the slope in this problem? 1981 1950.8 1981 1937.2 e) What percent of the observed variation in 1982 1895.3 the race times can be explained by your 1983 1895.0 model? 1983 1887.6 f) Find the residual for the first data point or 1984 1873.8 the list (the 2286.4 seconds from 1967). 1985 1859.4 g) What does this linear model predict for th race time in the year 2075? Do you think 1986 1813.7 this is reasonable?…

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t have a useful interpretation in this study? Why or why not. b. Interpret the effect of a unit increase in L