### Minitab Output Analysis#### IntroductionThis page presents an analysis of regression output generated from Minitab statistical software. This is useful for educational purposes to understand how to interpret regression results.#### Regression EquationThe regression equation provided by Minitab is:\[ \text{Highway} = 50.4 - 0.00543 \times \text{Weight} \]#### Coefficients and Statistics| Predictor | Coef | SE Coef | T | P ||------------|-----------|---------|-------|------|| Constant | 50.442 | 2.896 | 17.45 | 0.000|| Weight | -0.0054268| 0.0007554 | -7.05 | 0.000|- **S = 2.14999**- **R-Sq = 63.2%**- **R-Sq (adj) = 60.4%**##### Explanation:- **Coef:** The coefficients of the regression equation. - Constant: 50.442 - Weight: -0.0054268- **SE Coef:** Standard Error of the coefficient.- **T:** T-statistic for the hypothesis test.- **P:** P-value for the hypothesis test (indicating statistical significance).The negative coefficient for Weight suggests that as weight increases, Highway mileage decreases.#### Predicted Values for New ObservationsDetails on the predicted values for new observations are as follows:| New Obs | Fit | SE Fit | 95% CI | 95% PI ||---------|--------|--------|-------------------|-------------------|| 1 | 34.162 | 0.518 | (33.159, 35.165) | (29.566, 38.758) |**Values of Predictors for New Observations**| Obs | Weight ||-----|--------|| 1 | 3000 |This section provides the predicted Highway value when Weight is 3000 along with confidence intervals (CI) and prediction intervals (PI).- **Fit:** The predicted value.- **SE Fit:** The standard error of the predicted value.- **95% CI:** The 95% confidence interval for the mean response.- **95% PI:** The 95% prediction interval **Understanding Linear Correlation Coefficient in Highway Fuel Consumption**The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 29 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 29 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts?[Click the icon to view the Minitab display.]**The linear correlation coefficient is [ ].**(Round to three decimal places as needed.)---*Interactive Elements:*- Help me solve this- View an example- Get more help[Clear all | Check answer]---**Explanation of Graphs/Diagrams:**There are no specific graphs or diagrams provided in this particular image. However, it mentions "Click the icon to view the Minitab display," suggesting that the Minitab display, which likely contains the necessary statistical data for analysis, is available upon clicking an icon in the interface.For educational purposes, understanding how to interpret a Minitab output is crucial. Typically, such outputs will provide values for the linear correlation coefficient, which measures the strength and direction of the linear relationship between two variables. Values close to 1 or -1 indicate a strong linear relationship, while those close to 0 suggest a weak or no linear relationship.

Given: The coefficient of determination R2 = 63.2% R2 = 0.632 Formula Used: Correlation…

Answered: The Minitab output shown below was…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A random sample of college students was surveyed about how they spend their time each week. The scatterplot below displays the relationship between the number of hours each student typically works per week at a part- or full-time job and the number of hours of television each student typically watches per week. The correlation between these variables is r = –0.63, and the equation we would use to predict hours spent watching TV based on hours spent working is as follows: Predicted hours spent watching TV = 17.21 – 0.23(hours spent working) Since we are using hours spent working to help us predict hours spent watching TV, we’d call hours spent working a(n) __________________ variable and hours spent watching TV a(n) __________________ variable. The correlation coefficient, along with what we see in the scatterplot, tells us that the relationship between the variables has a direction that is _________________ and a strength that is ______________________. According to the…
An ecologist is interested in exploring the relationship between pollination rate and the number of bees present at apple orchards. The relationship is: (Pollination rate) = 372.6 + 13.5 x (bees) with r = 0.80. The best interpretation of the correlation coefficient is: (pick one) 1. 64% of the variability in pollination rate observed at apple orchards is explained by the relationship with the number of bees 2. the correlation between pollination rate and number of bees is 0.64 3. 80% of the variability in number of bees at apple orchards is explained by the relationship with the pollination rate 4. the correlation between pollination rate and number of bees is 0.80
Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a = 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? Lemon Imports Crash Fatality Rate 228 264 358 482 531 15.9 15.7 15.5 15.3 14.9
A veterinarian collects data about puppies in her practice. She makes a scatterplot with their age in days on the horizontal axis and weight in ounces (oz) on the vertical axis and sees that the scatterplot is football shaped. The average age of the puppies is 42 day, with an SD of 7 days. The average weight is 25 oz, with an SD of 5 oz. The correlation is moderately strong, with r = 0.7. 4. (a) The age of two puppies differ by 20 days. The difference in their weight is predicted to be oz. (b) The baseline prediction for the weight of puppies ignores their age and just uses the information from all puppies. The baseline predicted weight is oz and the RMS error for this prediction is o. (c) Suppose we converted the units of age from days to weeks. The average age is now weeks, with an SD of weeks. The correlation between age in weeks and weight in oz is now r =
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 31 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 4000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 31 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Click the icon to view the Minitab display. The linear correlation coefficient is (Round to three decimal places as needed.) Is there sufficient evidence to support a claim of linear correlation? Yes O No Minitab output The regression equation is Highway = 50.8 -0.00508 Weight Predictor Coef SE Coef T P Constant 50.772 2.793…
The Minitab output shown below was obtained by using paired data consisting of weights (in lb) of 26 cars and their highway fuel consumption amounts (in mi/gal). Along with the paired sample data, Minitab was also given a car weight of 3000 lb to be used for predicting the highway fuel consumption amount. Use the information provided in the display to determine the value of the linear correlation coefficient. (Be careful to correctly identify the sign of the correlation coefficient.) Given that there are 26 pairs of data, is there sufficient evidence to support a claim of linear correlation between the weights of cars and their highway fuel consumption amounts? Click the icon to view the Minitab display. The linear correlation coefficient is (Round to three decimal places as needed.) Minitab output The regression equation is Highway = 50.3 -0.00539 Weight Predictor Coef SE Coef Constant 50.288 2.998 Weight -0.0053868 0.0007773 |S=2.11773 R-Sq=64.0% R-Sq(adj) = 60.9% Predicted Values…
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using a = 0.05, Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.5 178 Click here to view a table of critical values for the correlation coefficient. 9.6 9.4 8.8 8.2 Weight 112 205 238 204 188 OA. YB. OC. KD D. Aweight (kg) 300- A weight (kg) Aweight (kg) 300- Aweight (kg) 300- 300- .. 100 100+ 100 7. rect: 0 10 10 10 10 width (om) width (cm) width (on) widn (om) The linear correlation coefficient is r= (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. O parts remaining Check Answer वी
Listed below are annual data for various years. The data are weights (metric tons) of imported lemons and car crash fatality rates per 100,000 population. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value using a= 0.05. Is there sufficient evidence to conclude that there is a linear correlation between lemon imports and crash fatality rates? Do the results suggest that imported lemons cause car fatalities? Lemon Imports Crash Fatality Rate 266 15.7 228 358 484 531 15.8 15.5 15.2 14.8 What are the null and alternative hypotheses? O B. Ho: p=0 O A. Ho: p#0 H1:p=0 H1:p0 H,: p#0 Construct a scatterplot. Choose the correct graph below. OA. B. Oc. OD. Ay 17- Ay 17- AY 17- Ay 17- 16- Q 16- 16- 16- 15- 15- 15- 15- 14- 14+ 14- 14- 200 400 600 200 400 600 200 400 6ỏ0 200 400 600 The linear correlation coefficient is r= (Round to three decimal places as needed.)
Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using a = 0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.2 7.5 9.8 9.3 8.9 8.1 Weight 119 172 248 201 205 181 Click here to view a table of critical values for the correlation coefficient. Construct a scatterplot. Choose the correct graph below. A. В. OC. D. Aweight (kg) 300- Aweight (kg) 300- Aweight (kg) 300- Aweight (kg) 300- 100+ 1004 100- 100+ 10 7 10 7 10 7 10 width (cm) width (cm) width (cm) width (cm) The linear correlation coefficient is r= (Round to three decimal places as needed.) The critical values are r= (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute…
The National Longitudinal Study of Adolescent Health interviewed several thousand teens (grades 7 to 12). One question asked was “What do you think are the chances you will be married in the next 10 years?” Here is a two-way table of the responses by gender: Opinion Female Male Almost no chance 120 94 Some chance but probably not 156 178 A 50-50 chance 427 498 A good chance 750 700 Almost certain 1176 770 How many individuals are described in this table? How many females were among the respondents? The percent of females among the respondents was about %. Your percent from the previous exercise is part of the marginal distribution of opinion about marriage. the conditional distribution of sex among adolescents with a given opinion. the marginal distribution of sex. What percent of females thought that they were almost certain to be married in the next 10 years?% Your percent from the previous exercise is part of the conditional distribution of sex among…
Complete the following instructions:i. Identify the independent and dependent variables.ii. Calculate and interpret the Pearson correlation coefficient r for the paired data. Be sure to indicate if the correlation is positive or negative, and whether it is strong, moderate, or weak, or if there does not appear to be any significant correlation. A researcher for a gasoline retailer examines the relationship between the volume of gasoline purchased in kL(i.e. 1000 L) compared to the price of gasoline (in $/L), over a course of several days, to see if there is a correlation between the data: Amount of Gasoline Purchased Price of Gasoline 2.257 1.079 3.126 1.015 2.793 1.046 4.671 0.973 2.137 1.021 5.916 0.939 2.775 0.995 4.88 0.927 3.162 0.964 7.498 0.899 2.971 0.982 3.596 0.945 1.372 1.129 3.961 1.059 i. Independent Variable: Dependent Variable: ii. Pearson correlation coefficient (r): Round to 3 decimal…

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