### Regression Analysis Example**Problem Statement:**The following estimated regression equation is based on 30 observations.\[\hat{y} = 18.1 + 3.9x_1 - 2.1x_2 + 7.8x_3 + 2.8x_4\]The values of SST (Total Sum of Squares) and SSR (Sum of Squares for Regression) are 1,801 and 1,762, respectively.**Tasks:**a. **Compute \(R^2\) (to 3 decimals).**b. **Compute \(R^2_{\text{adj}}\) (to 3 decimals).**c. **Comment on the goodness of fit.****Solution:**a. To compute \(R^2\):\[R^2 = \frac{\text{SSR}}{\text{SST}} = \frac{1,762}{1,801} \approx 0.978\]Incorrect entry: \[ \]b. To compute \(R^2_{\text{adj}}\):\[R^2_{\text{adj}} = 1 - \left(\frac{1 - R^2}{n - k - 1} \times (n - 1)\right) \]Where:- \( n \) is the number of observations (30)- \( k \) is the number of predictors (4)So,\[R^2_{\text{adj}} = 1 - \left(\frac{1 - 0.978}{30 - 4 - 1} \times (30 - 1)\right) \]Incorrect entry: \[ \]c. Comment on the goodness of fit:The estimated regression equation provided an excellent fit.Correct selection: \[\boxed{\text{provided an excellent fit}}\]Explanation: - **Hint:** Use the provided results and formulas for calculating the coefficients of determination to evaluate the regression model.- **Feedback:** Partially correct. Ensure the correct values are entered for theoretical completeness.**Graph/Diagram Explanation:**No graphs or diagrams are present in this example.---This form of transcription can serve as an understanding aid for students studying regression analysis, helping them to correctly apply and interpret the formulas involved. This example elucidates the process of computing both \(R^2\) and \(R

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Answered: The following estimated regression…

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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You may need to use the appropriate technology to answer this question. A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information. ŷ = 0.406 + 1.3385x₁ + 2x₂ The SSE for the above model is 43. When two other independent variables were added to the model, the following information was provided. ŷ = 1.9 - 3x₁ + 12x2 + 4x3 + 8x4 This model's SSE is 36. At a 0.05 level of significance, test to determine if the two added independent variables contribute significantly to the model. State the relevant null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = P₂ = P3 =B4 = 0 B1 O Ho: One or more of the parameters is not equal to zero. H₂: B3 =B₁ = 0 O Ho: B3 = P4 = 0 H₂: None of the parameters are equal to zero. O Ho: B3 B4= = = H₂: One or more of the parameters is not equal to zero. O Ho: P₁ = P₂ = P3= P4= H: One or more of the parameters is not equal to zero. Find…
The datasetBody.xlsgives the percent of weight made up of body fat for 100 men as well as other variables such as Age, Weight (lb), Height (in), and circumference (cm) measurements for the Neck, Chest, Abdomen, Ankle, Biceps, and Wrist. We are interested in predicting body fat based on abdomen circumference. Find the equation of the regression line relating to body fat and abdomen circumference. Make a scatter-plot with a regression line. What body fat percent does the line predict for a person with an abdomen circumference of 110 cm? One of the men in the study had an abdomen circumference of 92.4 cm and a body fat of 22.5 percent. Find the residual that corresponds to this observation. Bodyfat Abdomen 32.3 115.6 22.5 92.4 22 86 12.3 85.2 20.5 95.6 22.6 100 28.7 103.1 21.3 89.6 29.9 110.3 21.3 100.5 29.9 100.5 20.4 98.9 16.9 90.3 14.7 83.3 10.8 73.7 26.7 94.9 11.3 86.7 18.1 87.5 8.8 82.8 11.8 83.3 11 83.6 14.9 87 31.9 108.5 17.3…
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05 Right Arm 101 100 94 75 Left Arm 174 167 146 144 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is (Round to one decimal place as needed.) 76 144 CRITS
You may need to use the appropriate technology to answer this question. A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information. ý = 0.406 + 1.3385X + 2X2 The SSE for the above model is 43. When two other independent variables were added to the model, the following information was provided. ŷ = 1.9 - 3x₁ + 12x₂ + 4x3 + 8x4 This model's SSE is 36. At a 0.05 level of significance, test to determine if the two added independent variables contribute significantly to the model. State the relevant null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = B₂= B3 = P4 = 0 OH: One or more of the parameters is not equal to zero. H₂: B3 =B₁ = 0 O Ho: B3 =B4 = 0 H₂: None of the parameters are equal to zero. H₁: B3 =B4 = 0 H₂: One or more of the parameters is not equal to zero. O Ho: B₁ = B₂= B3 =B4 = 0 H₂: One or more of the parameters is not equal to zero. ✔ Find the…
Using 23 observations on each variable, a computer program generated the following multiple regression model. y = 65.5 +9.56x1+3.27x2-4.23x3– 9.23x4 If the standard errors of the coefficients of the independent variables are, respectively, 3.44, 2.30, 2.76, and 4.99, can you conclude that the independent variable x, is needed in the regression model? Let B1, B2, Ba denote the coefficients of the 4 variables in this model, and use a two-sided hypothesis test and significance level of 0.10 to determine your 4 .../ answer. (a) State the null hypothesis H, and the alternative hypothesis H,. H, : 0 H, : 0 (b) Determine the type of test statistic to use. Degrees of freedom: D=0 OSO (c) Find the value of the test statistic. (Round to two or more decimal places.) O#0 OO (d) Find the two critical values at the 0.10 level of significance. (Round to two or more decimal places.) | and || (e) Can you conclude that the independent variable is needed in the regression model? Yes No 미
Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 85 mm Hg. Use a significance level of 0.05 Right Arm 101 100 94 75 Left Arm 174 167 146 144 Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is (Round to one decimal place as needed.) 76 144 CRITS
You may need to use the appropriate technology to answer this question. A regression analysis involving 45 observations relating a dependent variable and two independent variables resulted in the following information. ý = 0.406 + 1.3385X, + 2X2 The SSE for the above model is 43. When two other independent variables were added to the model, the following information was provided. ý = 1.9 – 3X + 12X2 + 4Xg + 8x, This model's SSE is 36. At a 0.05 level of significance, test to determine if the two added independent variables contribute significantly to the model. State the relevant null and alternative hypotheses. O Ho: One or more of the parameters is not equal to zero. H₂: B₁ = B₂= B3 =B4 = 0 O Ho: One or more of the parameters is not equal to zero. H₂: B3 =B4 = 0 O Ho: B3 = P4 = 0 H₂: None of the parameters are equal to zero. ⒸH₁: B3 =B₁ = 0 H: One or more of the parameters is not equal to zero. O Ho: B₁ = P₂ = B3 =B4 = 0 H: One or more of the parameters is not equal to zero. ✔ Find…
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Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is Price = B + ¢Bedroom + yHouse Size + ALot Size Predictor Сoef SE Coef т P Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 0.164 Lot Size -4.36 17.02 -0.26 0.798 S= 25023 R-Sq=56.0% R-Sq(adj)=54.6% Source DF MS F P Regression 3 76501718347 25500572782 Residual Error 96 60109046053 626135896 Total 99 • Is y significantly different from -0.5? Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. Give an interpretation to the term “R-sq" and comment on its value.
The accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. (a) x = 5 wins Click the icon to view the table of numbers of wins and earned run average. (b) x= 10 wins (c) x=21 wins (d) x= 15 wins The equation of the regression line is y = x+ | (Round to two decimal places as needed.) !!
Find the new data point (x,y) in which x=2 from the data points (1.3) and (4.12)
Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sg ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract: The regression equation is Price = B + ÞBedroom + yHouse Size + ALot Size Predictor Coef SE Coef T P Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 0.164 Lot Size -4.36 17.02 -0.26 0.798 s= 25023 R-Sq=56.0% R-Sq(adj)=54.6% Source DF MS F P Regression Residual 3 76501718347 25500572782 **** Error 96 60109046053 626135896 Total 99 1. Fill in the missing values *, **, and **** 2. Use the p-value approach to determine if o is significant at the 5% significance level

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