### Study on the Relationship Between Education and Yearly Income in Californians Over 30A survey is conducted on 700 Californians older than 30 years of age. The study aims to obtain inference on the relationship between years of education and yearly income in dollars. The response variable is income in dollars, and the explanatory variable is years of education.A simple linear regression model is fit, and the output from R is below:```Rlm(formula = Income ~ Education, data = CA)```**Coefficients:**| | Estimate | Std. Error | t value | Pr(>|t|) ||--------------|----------|------------|---------|---------------------|| (Intercept) | 25200.25 | 1488.94 | 16.93 | 3.08e-10 *** || Education | 2905.35 | 112.61 | 25.80 | 1.49e-12 *** |**Additional Model Information:**- **Residual standard error:** 32400 on 698 degrees of freedom- **Multiple R-squared:** 0.7602**Explanation of Results:**- **Intercept (25200.25):** This is the estimated income (in dollars) for a person with zero years of education.- **Education (2905.35):** This coefficient indicates the increase in yearly income (in dollars) for each additional year of education. In this case, each additional year of education corresponds to an increase of approximately $2905.35 in yearly income. **Significance Codes:**The significance codes indicate the statistical significance of the coefficients. Generally, the smaller the p-value, the stronger the evidence against the null hypothesis, suggesting that the coefficient is not zero and the variable has a meaningful impact on the response variable.- '***': p-value < 0.001 : Highly significant **Question:**Assume someone can have 0 years of education. Does the intercept have a useful interpretation? And if so, what is that interpretation?**Answer Options:**1. ( ) No useful interpretation.2. ( ) Yes, it is the estimated expected income of someone with 1 year of education.3. ( ) Yes, it is the estimated expected income of someone with 0 years of education.4. ( ) Yes, it is the estimated expected income of someone with the most years of education.

The intercept of regression line tells that the estimated value of dependent variable when the…

Answered: A survey is conducted on 700…

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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The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Studying 0.5 1 1.5 2 3 3.5 4.5 Midterm Grades 63 66 68 72 74 93 94 Table Step 4 of 6 : Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.
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The manager of the Bayville police department motor pool wants to develop a forecast model for annual maintenance on police cars, based on mileage in the past year and age of the cars. The following data have been collected for eight different cars: a. Using Excel, develop a multiple regression equation for these data. b. What is the coefficient of determination for this regression equation? c. Forecast the annual maintenance cost for a police car that is 5 years old and will be driven 10,000 miles in 1 year.
The table below gives the number of hours seven randomly selected students spent studying and their corresponding midterm exam grades. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the midterm exam grade that a student will earn based on the number of hours spent studying. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Studying 1 1.5 2 2.5 3 3.5 4.5 Midterm Grades 61 62 75 77 79 83 88 Table Step 1 of 6 : Find the estimated slope, y intercept and correlation cofficient. Round your answer to three decimal places.
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 88 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−0.813+0.177?,h^=−0.813+0.177w, with standard error for the coefficient of ?w equal to 0.448. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
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Suppose that you are interested in the relationship between Reading and Writing scores. (c) Compute and interpret the R2 value for the relationship between Reading and Writing scores. (d) Interpret the value of the slope in the regression model predicting Reading scores from Writing scores. RDG WRTG 34 44 47 36 42 59 39 41 36 49 50 46 63 65 44 52 47 41 44 50 50 62 44 41 47 40 42 59 42 41 47 41 60 65 39 49 57 54 73 65 47 46 39 44 35 39 39 41 48 49 31 41 52 63 47 54 36 44 47 44 34 46 52 57 42 40 37 44 44 33 71 58 47 46 42 33 42 36 47 41 52 54 52 54 39 39 31 41 60 54 47 31 39 28 42 36 47 57 42 49 36 41 50 33 34 34 55 55 28 46 42 42 44 44 60 52 39 57 36 37 44 44 39 42 39 34 42 39 42 44 52 54 65 65 42 26 47 62 52 62 44 54 52 54 47 44 65 57 63 65 60 59 47 44 65 57 53 61 68 63 55 56 39 53 52 52 65 67 52 44 57 67 63…
According to an article, one may be able to predict an individual's level of support for ecology based on demographic and ideological characteristics. The multiple regression model proposed by the authors was the following. y = 3.60-.01x₁+.01.₂-.07x3+.12x4+.02xs-.04x6-01-.04.xg-.02.xg+c The variables are defined as follows. y = ecology score (higher values indicate a greater concern for ecology) X₁ = age times 10 x₂ = income (in thousands of dollars) x3 = gender (1 = male, 0 = female) X4 = race (1 = white, 0 = nonwhite) X5 = education (in years) x6 = ideology (4 = conservative, 3 = right of center, 2 = middle of the road, 1 = left of center, and 0 = liberal) X7 = social class (4 = upper, 3 = upper middle, 2 = middle, 1 = lower middle, 0 = lower) xg = postmaterialist (1 if postmaterialist, 0 otherwise) x9 = materialist (1 if materialist, 0 otherwise) (a) Suppose you knew a person with the following characteristics: a 30 year old, white female with a college degree (20 years of…
Stoaches are fictional creatures that nest in truffula forests. A researcher wants to know whether there is a relationship between a stoach’s wingspan (?W, the predictor) and its nest height (?H, the response). A sample of 85 stoaches is observed, and for each, the wing-span (in cm) and the nest height (in m) are recorded. The observed data meet the assumptions for a linear regression, so the researcher fits the regression model and obtains a regression equation ℎ̂=−4.273+0.834?,h^=−4.273+0.834w, with standard error for the coefficient of ?w equal to 0.242. Determine the ?p-value from a test for a statistically significant linear dependence of nest height on wing-span. (Give your answer to 4 decimal places.
Do movies of different types have different rates of return on their budgets? Here's a regression of USGross (SM) on Budget for comedies and action movies with an indicator variable. Complete parts (a) through (d). Dependent variable is: USGross ($M) Coefficient SE(Coeff) - 6.78278 16.95 1.00523 Variable Constant Budget ($M) Comedy 24.0373 0.1613 11.73 t-ratio P-value -0.400 0.6907 6.23 <0.0001 2.05 0.0451 a) Write out the regression model. USGross = + ( Budget + (Comedy R-squared = 32.8% R-squared (adjusted) = 31.0% s = 47.51 55 degrees of freedom
Are the years of education of a child dependent on the years of education of their parent? The table shows the number of years of education of parent and the number of years of education of their child. Years of Education of Parent 13 9 7 12 12 10 11 Years of Education of their Child 13 11 7 16 17 9 17 If there is a significant linear correlation between the variables, determine the regression equation. Are the years of education of a child dependent on the years of education of their parent? The table shows the number of years of education of parent and the number of years of education of their child. Years of Education of Parent 13 9 7 12 12 10 11 Years of Education of their Child 13 11 7 16 17 9 17 If there is a significant linear correlation between the variables, determine the regression equation. y’ = 1.5x - 3 There is no significant correlation between the variables,…

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