Suppose the number of seconds required to accelerate to 60 mph depends on both a car’s weight, its horsepower, and an interaction term between the two variables.Describe why an interaction term could be appropriate for the variables in this model and construct three linear relationships between acceleration time and weight, each for a different assumed value of horsepower. ### Summary Output#### Regression Statistics- **Multiple R:** 0.856730669- **R Square:** 0.733987439- **Adjusted R Square:** 0.687044045- **Standard Error:** 2.967605917- **Observations:** 21#### Analysis of Variance (ANOVA)| | df | SS | MS | F | Significance F ||----------|----|------------|------------|------------|---------------------|| Regression | 3 | 413.0930237 | 137.6976746 | 15.63558552 | 3.87427E-05 || Residual | 17 | 149.7136429 | 8.806688479 | | || Total | 20 | 562.8066667 | | | |#### Coefficients| | Coefficients | Standard Error | t Stat | P-value ||--------------|----------------|----------------|-------------|---------------|| Intercept | 25.41936066 | 4.338034616 | 5.859649107 | 1.89327E-05 || hp | -0.161091493 | 0.035506341 | -4.536978136 | 0.000291759 || curbwt | -0.000302296 | 0.002232767 | -0.135390557 | 0.893893295 || hp*curbwt | 2.8177E-05 | 9.4596E-06 | 2.978662513 | 0.008429352 |### ExplanationThis output is from a multiple regression analysis, indicating the relationship between a dependent variable and several independent variables. - **Multiple R** and **R Square** indicate the strength and proportion of variance explained by the model.- **Adjusted R Square** accounts for the number of predictors in the model.- **ANOVA** table shows the breakdown of variances, with a significant F-statistic suggesting the model is a good fit.- **Coefficients** table provides the estimated impact of each predictor, with associated statistical tests. Lower p-values suggest significant contributions to the model.

Let 'y' denotes the number of seconds required to accelerate to 60 mph. 'hp' denotes the horsepower of the car and 'curbwt' denotes the weight of the car. According to the given ANOVA table, the linear model which gives the estimate of the number of seconds required to accelerate to 60 mph is as follows: y^=25.41396066 - 0.161091493×hp - 0.000302296×curbwt + 0.000028177×hp×curbwtThe interaction term: Although the coefficient of the interaction term is very small, yet the interaction term is important because firstly it is significant in the model. The P-Value of the interaction term is <0.01 which indicates that it is significant at 1% level of significance. Also as the dependent variable is measured in seconds, small value of the interaction term will also be impactful when comparing various models of car. Hence, we should keep interaction term in the model. Let us assume the following values of horsepower: hp = 200 hp = 250 hp = 300 Case 1: hp = 200 The linear model is: y^1=25.41396066 - 0.161091493×200 - 0.000302296×curbwt + 0.000028177×200×curbwty^1=-6.804338+0.005333104×curbwt Case 2: hp = 250 The linear model is: y^2=25.41396066 - 0.161091493×250 - 0.000302296×curbwt + 0.000028177×250×curbwty^2=-14.8589126+0.00674195×curbwt Case 3: hp = 300 The linear model is: y^3=25.41396066 - 0.161091493×300 - 0.000302296×curbwt + 0.000028177×300×curbwty^3=-22.91348724-0.008150804×curbwt Hence, the three linear relationships are denoted by y^1,y^2 and y^3.

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Suppose the number of seconds required to accelerate to 60 mph depends on both a car’s weight, its horsepower, and an interaction term between the two variables. Describe why an interaction term could be appropriate for the variables in this model and construct three linear relationships between acceleration time and weight, each for a different assumed value of horsepower.

Suppose the number of seconds required to accelerate to 60 mph depends on both a car’s weight, its horsepower, and an interaction term between the two variables. Describe why an interaction term could be appropriate for the variables in this model and construct three linear relationships between acceleration time and weight, each for a different assumed value of horsepower.

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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