**Problem 4. (Scaling)** Consider the linear regression model in which\[Y = X\boldsymbol{\beta} + \boldsymbol{\varepsilon}\]under our standard assumptions with $p - 1$ predictors. Suppose that we scale the explanatory variables so that $x_{ij} = k_jw_{ij}$, where $i = 1, ..., n$, $j = 1, ..., p$. By expressing $\mathbf{X}$ in terms of $\mathbf{W}$, prove that $\mathbf{Y}$ remains unchanged under this change of scale. How do the new coefficients $\boldsymbol{\beta}^W$ with $W_j$ as predictors compare to coefficients $\boldsymbol{\beta}^X$, with $\mathbf{X}$ as predictors?

The linear regression model is: Y=Xβ+ε....................(1)Y^=Xβ........................(2)

Answered: Problem 4. (Scaling) Consider the…

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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Q2. The Update to the Task Force Report on Blood Pressure Control in Children reported the observedaverage SBP in single years of age from age 1 to 17 based on prior studies. The data for boys of averageSBP at each age are given in HW 5 data.sav on Blackboard. Suppose we seek a more efficient way todisplay the data and choose linear regression to accomplish this task.1) Fit a regression line using age as independent variable and SBP as dependent variable. (Theappropriate output is required here if you used software)2) Interpret the regression equation.3) Provide and interpret a 90% confidence interval for the parameters of the regression line.4) Perform ANOVA test for the population slope. Use α = 0.05, and both rejection region and p-value to make a decision.5) What the predicted (estimated) blood pressure on average is for a 10-year-old boy as estimatedfrom the regression line?6) Interpret R2.7) Check the conditions for your regression analysis using the appropriate plots. Age…
please give me the right answer for both of thesd problem by fallowing the format too please
3. Given the following regression: Wage = 10 + 1.2 x male + 2 x educ + 0.15 x (male x educ) + u The dependent variable is hourly wage. There are three independent variables: a binary variable indicating male, years of education, and an interaction between male and educ. (a) Plot the relationship between wage and education for males and females separately. Put wage on the vertical axis and education on the horizontal axis. (hint: see Panel (b) of Figure 8.8 in the textbook; You may draw the graph on software or on a piece of paper and paste the snapshot below.) (b) According to the regression function above, (1) which gender has a higher base wage (for people with no education)? (2) which gender has higher return to education? (3) what's effect of an additional year of education on wage for females? (4) what's the effect of an additional year of education on wage for males? On * Accessibility: Investigate
19. We are interested in the relationship between years of post-secondary education (x), and annual salary (y), so a survey is put together and the linear regression analysis yields an R2 value of .79 the following regression line: ŷ = 4,500x + 40,000 b) What is the correct interpretation of the slope? Group of answer choices A person with 0 years of post-secondary education can expect a salary of $40,000 79% of the variation found in salary can be explained by variation in years of post-secondary education For every additional year of post-secondary education, the expected annual salary increases by $4,500 There is a strong, positive, linear correlation between years of post-secondary education and annual salary.
4. In multiple regression, why do we prefer our IVs to be uncorrelated with each other (i.e., we want rx, x, to be 0)?
4. Our R² implies that lots of stuff, other than health, also affects doctor visits. One such thing is a person's insurance status. The data file includes a third variable that records whether the person had health insurance during 2019. Estimation a regression of the form y = Bo + B₁x1 + B₂x₂ where x₁ is the health status variable from above, but now x₂ records whether the person had insurance. a) Interpret the estimate of B₁ in words. b) Interpret the estimate of B₂ in words. c) Forecast a person's number of doctor visits in 2019 if he/she was in excellent health, but did not have insurance. d) Forecast a person's number of doctor visits in 2019 if he/she was in poor health, and did have insurance. e) The R² for this regression is
7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannel
1
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
In this problem you will perform calculations by hand, do not use the R functions lm() or anova() to find the results. Suppose our sample data consists of the six (x,y) pairs {(2,5), (4,6), (5,5), (7,10), (8,9), (10,13)}. Find Determine the fitted regression equation for this data, and use it to predict y for x=2, 4, 5, 7, 8, and Find the error associated with each of these predictions. Find Use the results from part (a) and (c) to calculate the coefficient of determination. What percentage of the variation in y is explained by the regression?
Question 12. Fit a regression line to the points (2, 7), (3, –3), (–2, 5).

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