Like father, like son: In 1906, the statistician Karl Pearson measured the heights of 1078 pairs of fathers and sons. The following table presents a sample of 6pairs, with height measured in inches, simulated from the distribution specified by Pearson.Father's Son'sheight height70.869.870.770.1 73.373.6 76.565.772.471.0Part: 0 / 470.9Send data to ExcelPart 1 of 469.1The least-squares regression line y = b + b₁ x = 47.8026+0.3397x and Σ (x-x)² = 36.5350 are known for this data. Use the critical value method to testH₂ :B₁ = 0 versus H₁ :B₁ +0. Can you conclude that the father's height is useful in predicting the son's height? Use the α = 0.01 level of significance.Find the critical value(s). Round the answer to three decimal places. If there is more than one critical value, separate them with commas.Critical value(s):0,0,...

Given,the father's height and the son's height.Also, the regression line is given.To test the…

Answered: he least-squares regression line y=bo…

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 regression model involving 8 independent variables for a sample of 69 observations resulted in the following sum of squares. SSE = 306 SST = 1800 Compute the multiple coefficient of determination. At 5% of level of significance, test to determine whether or not the model is significant. Question 3: A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Write out the estimated regression equation for the relationship between the variables. Compute coefficient of determination. Can you interpret the strength of the…
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings(x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Coefficients Standard Error Intercept 0.0136 x 1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 Required: c. Carry out a test to determine whether y is significantly related to the independent variables. Use a 5% level of significance. d. Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
A baseball enthusiast carried out a simple linear regression to investigate whether there is a linear relationship between the number of runs scored by a player and the number of times the player was intentionally walked. Computer output from the regression analysis is shown. Variable DF Estimate SE Intercept 1 16 2.073 Intentional Walks 1 0.50 0.037 R-sq=0.63R-sq=0.63 Let β1β1 represent the slope of the population regression line used to predict the number of runs scored from the number of intentional walks in the population of baseball players. A tt-test for a slope of a regression line was conducted for the following hypotheses. H0:β1=0Ha:β1≠0 below are the options provided thank you
A regression model to predict Y, the state burglary rate per 100,000 people for 2005, used the following four state predictors: X1 = median age in 2005, X2 = number of 2005 bankruptcies, X3 = 2004 federal expenditures per capita (a leading predictor), and X4 = 2005 high school graduation percentage. (a) Fill in the values in the table given here for a two-tailed test at α = 0.01 with 33 d.f. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-values to 4 decimal places.) Predictor Coefficient SE tcalc p-value Intercept 4,579.5465 791.5050 AgeMed -27.292 12.1893 Bankrupt 19.5612 12.0754 FedSpend -0.0132 0.0116 HSGrad% -27.5839 7.1731 (b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at α = .01 with 33 d.f? (Round your answer to 3 decimal places.) t-value = (b-2) Choose the correct option.…
Write the multiple regression equation for miles per gallon as the response variable. How might the car rental company use this model?
Compute the least-squares regression line for predicting y from x given the following summary statistics. Round the slope and y -intercept to at least four decimal places. =x8.2 =sx3 =y1350 =sy13,000 =r0.40
1)Write the regression equation that represents the above equation. Y = 9.804326378 + 0.65795*X1 + 0.200358 X2 Height of an individual = 9.8043 + 0.6579*Mother's Height + 0.2004* Father's Height 2)Is this a good predictor equation? Why or why not (use appropriate statistics/hypothesis test to prove your point)?
In a study, data collected for 40 observations were used to model the dependent variable y with 8 independent variables under consideration, x1, x2, .. , Xg. Consider a stepwise regression run on the data. 1. What is the form of the model fit in step 1? How many models are fit? How is the "best" independent variable selected in this step? 2. What is the form of the model fit in step 2? How many models are fit? How is the "best" independent variable selected in this step? 3. What is the form of the model fit in step 3? How many models are fit? How is the "best" independent variable selected in this step? 4. The variables x3, x4, and x6 were deemed the best variables for predicting y. How do you recommend the researchers proceed from here? Why?
An article described an experiment carried out to assess the impact of the variable x₁ = force (gm), x₂ = power (mW), x3 = temperature (°C), and time (msec) on y ball bond shear strength (gm). X4 = = The estimated regression equation is y = -37.48 +0.2117x₁ +0.4983x2 +0.1297x3 +0.2583x4 Interpret b3 and b4. ● What is the expected value of strength (y) from a force of 35 gm, power of 75 mW, temperature of 200 °C, and time of 20 msec ?
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA df SS Regression 3 45.9634 Residual 11 2.6218 Total Coefficients Standard Error intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 answer please : 1: Carry out a test to see if x3 and y are significantly related. Use a 5% level of significance.
A linear regression model based on a random sample of 36 observations on the response variable and 4 predictors has a multiple coefficient of determination equal to 0.697. What is the value of the adjusted multiple coefficient of determination?
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