### Statistical Analysis Using Regression and Hypothesis Testing**Data Overview:**The table of data consists of two variables, \( x_i \) and \( y_i \):| \( x_i \) | 1 | 2 | 3 | 4 | 5 ||-----------|---|---|---|---|---|| \( y_i \) | 4 | 8 | 6 | 11 | 13 |**Analysis Steps:**1. **Compute the Mean Square Error (MSE):** - Use the formula \( s^2 = \text{MSE} = \dfrac{\text{SSE}}{n-2} \). - Answer: 3.84 (incorrect).2. **Compute the Standard Error of the Estimate:** - Use the formula \( s = \sqrt{\text{MSE}} = \sqrt{\dfrac{\text{SSE}}{n-2}} \). - Answer: 1.958 (incorrect).3. **Compute the Estimated Standard Deviation of \( b_1 \):** - Use the formula \( s_{b_1} = \dfrac{s}{\sqrt{\sum (x_i - \bar{x})^2}} \). - Answer: 0.619 (incorrect).4. **Use the t-test for Hypothesis Testing (α = 0.05):** - Hypotheses: - \( H_0: \beta_1 = 0 \) - \( H_a: \beta_1 \neq 0 \) - Test statistic = 4.038 (incorrect). - p-value = 0.0273 (incorrect). **Conclusion:** - Correct Decision: Reject \( H_0 \). The relationship between \( x \) and \( y \) is significant.5. **Use the F-test to Confirm Hypothesis at 0.05 Level of Significance:** - **ANOVA Table:** | Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value | |---------------------|----------------|--------------------|-------------|------|---------| | Regression | 62.5 | 1 | 62.5 | 16.3 | 0.027 | | Error | 11.5

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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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Using 50 observations, the following regression output is obtained from estimating y = 6g + 61x + 62d1 + 63dz + a. Standard Coefficients -0.75 2.86 -13.60 Error 0.30 1.10 t Stat -2.50 2.60 P-value 0.0160 0.0125 Intercept 16.00 -0.85 0.3997 d2 1.50 3.80 0.0004 5.70 a. Compute for x= 265, d 1, and d, = 0; compute for x 265, d1 = 0, and d, = 1. (Round your answers to 2 decimal places.) !! = 1 and d, 265, d1 265, d = 0 and d, = 1 b-1. Interpret d, and d2. (You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a wrong answer. Any boxes left with a question mark will be automatically graded as incorrect.) ?When d = 1, ý is 13.60 units greater than when d1 e, holding everything else constant. ?When d2 = 1, ŷ is 5.70 units greater than when d2 e, holding everything else constant. ?When d = 1, ŷ is 13.60 units less than when d1 0, holding everything else…
Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. Tinterval (13.046,22.15) x=17.598 Sx=16.01712719 n=50
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For variables X and Y we have that the correlation between them is 0.9. Also the standard deviation of Y is 8, while the standard deviation of X is 2. What is the slope of the regression equation that attempts to predict Y from X? Use two decimal places in your answer. Your Answer:
2. Below is the regression output from a model for predicting the heart weight (in g) of cats from their body weight (in kg). The coefficients are estimated using a dataset of 144 domestic cat. The model output is also provided below. Estimate Std. Error t value Pr(>|t|) (Intercept) body wt -0.357 0.692 -0.515 0.607 4.034 0.250 16.119 0.000 R2 64.66% Radi 64.41% s = 1.452 (a) We see that the point estimate for the slope is positive. What are Ho and HA for evaluating whether body weight is associated with heart weight in cats? (b) State the conclusion of the hypothesis test from part (a) in context of the data. (c) Calculate a 95% confidence interval for the slope of body weight, and interpret it in context of the data. (d) Do your results from the hypothesis test and the confidence interval agree? Explain.
Please do & explain with steps: Subparts e f & g please & thank u
4. Summary statistics for the data are shown in the table below. Меan Standard Deviation Iland, x 17.682 1.168 Foot, y 23.318 1.230 Pearson correlation r 0.948 (a) Find the slope by using the formula (b) Find the y-intercept by using the formula a = y – br (c) Find the regresssion equation, using the words "IHand" and "Foot," not r and y. (d) Using the regression equation, predict the foot length (in em) for someone who has a hand length of 18 cm.
Dont use excel. thanks
pls see attached
The regression line for Y vs X is given by Y = 0.82X + 59.1. The standard deviations for X and Y are 1.5 and 2.2 respectively. Suppose now we construct a regression line that uses Y to predict X. The predicted average increase of X when Y is increased by 1 unit is ______________. (Give your answer correct to 2 decimal places.)

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