Question

Call: lm(formula = mpg ~ hp + wt, data = mtcars) Residuals: Min 1Q Median 3Q Max -3.941 -1.600 -0.182 1.050 5.854 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 37.22727 1.59879 23.285 < 2e-16 *** hp -0.03177 0.00903 -3.519 0.00145 ** wt -3.87783 0.63273 -6.129 1.12e-06 *** --- Signif. codes: 0 β€˜***’ 0.001 β€˜**’ 0.01 β€˜*’ 0.05 β€˜.’ 0. Residual standard error: 2.593 on 29 degrees of freedom Multiple R-squared: 0.8268, Adjusted R-squared: 0.

          Call:
lm(formula = mpg ~ hp + wt, data = mtcars)
Residuals:
Min      1Q  Median      3Q     Max
-3.941 -1.600  -0.182   1.050   5.854
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.22727   1.59879  23.285  < 2e-16 ***
hp         -0.03177   0.00903  -3.519   0.00145 **
wt         -3.87783   0.63273  -6.129 1.12e-06 ***
---
Signif. codes:  0 β€˜***’ 0.001 β€˜**’ 0.01 β€˜*’ 0.05 β€˜.’ 0. 
Residual standard error: 2.593 on 29 degrees of freedom
Multiple R-squared:  0.8268,
Adjusted R-squared: 0.
        
Show more…
Call:
lm(formula = mpg Β  hp + wt, data = mtcars)
Residuals:
Min      1Q  Median      3Q     Max
-3.941 -1.600  -0.182   1.050   5.854
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 37.22727   1.59879  23.285  < 2e-16 ***
hp         -0.03177   0.00903  -3.519   0.00145 **
wt         -3.87783   0.63273  -6.129 1.12e-06 ***
β€”
Signif. codes:  0 β€˜***’ 0.001 β€˜**’ 0.01 β€˜*’ 0.05 β€˜.’ 0. 
Residual standard error: 2.593 on 29 degrees of freedom
Multiple R-squared:  0.8268,
Adjusted R-squared: 0.

Added by Marvin T.

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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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For the above model, what is the predicted miles per gallon for a car with 110 horsepower and that weighs 2.62 tons? Assume the model measures weight in tons. 3 sig digits Call: lm(formula = mpg ~ hp + wt, data = mtcars) Residuals: Min 1Q Median -3.941 -1.600 -0.182 3Q Max 1.050 5.854 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 37.22727 1.59879 23.285 < 2e-16 *** hp -0.03177 0.00903 -3.519 0.00145 ** wt -3.87783 0.63273 -6.129 1.12e-06 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Residual standard error: 2.593 on 29 degrees of freedom Multiple R-squared: 0.8268, Adjusted R-squared: 0.
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The following is the dummy variable regression results of MPGavg on Cyl_4Dum and Cyl_6Dum. Summary of Fit RSquare 0.7507 RSquare Adj 0.7456 Root Mean Square Error 1.7024 Mean of Response 21.2300 Observations (or Sum Wgts) 100 Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 2 846.5858 423.293 146.0543 Error 97 281.1242 2.898 Prob > F <.0001 C. Total 99 1127.7100 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept 16.9545 0.363 46.7126 <.0001 Cyl_4Dum 7.2455 0.4429 16.36 <.0001 Cyl_6Dum 3.0758 0.4686 6.5641 <.0001 Based on the regression results, solve for the predicted MPGavg for 8 cylinder cars.

Madhur L.

r-software-has-some-built-in-data-sets-for-this-question-we-will-use-the-mtcars-data-file-you-can-see-the-file-by-typing-in-mtcars-into-r-studio-to-see-a-preview-of-the-data-the-following-is-16263

R software has some built-in datasets. For this question, we will use the mtcars data file. You can see the file by typing in: mtcars into R Studio to see a preview of the data. The following is a summary of the dataset. mpg: information about the average miles per gallon the car gets. cyl: number of cylinders the car has. hp: the horsepower of the car. wt: the weight of the car in thousands of pounds. 1. Create a linear regression model to predict the mpg of the vehicle given its cyl, hp, and wt values. Provide the partial slope coefficient of the wt variable from the regression model developed. 2. In conducting a hypothesis test to determine whether the cyl variable is statistically significant, provide the t-test value to determine its significance. 3. For every unit increase in hp, how many units of decrease in mpg?

Sri K.

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from statsmodels.formula.api import ols # create the simple linear regression model with mpg as the response variable and weight as the predictor variable model = ols('mpg ~ wt', data=cars_df).fit() #print the model summary print(model.summary()) OLS Regression Results ============================================================================== Dep. Variable: mpg R-squared: 0.750 Model: OLS Adj. R-squared: 0.741 Method: Least Squares F-statistic: 84.05 Date: Wed, 05 Feb 2020 Prob (F-statistic): 6.32e-10 Time: 03:12:56 Log-Likelihood: -75.748 No. Observations: 30 AIC: 155.5 Df Residuals: 28 BIC: 158.3 Df Model: 1 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept 37.2297 1.931 19.282 0.000 33.275 41.185 wt -5.3002 0.578 -9.168 0.000 -6.484 -4.116 ============================================================================== Omnibus: 2.182 Durbin-Watson: 1.825 Prob(Omnibus): 0.336 Jarque-Bera (JB): 1.817 Skew: 0.587 Prob(JB): 0.403 Kurtosis: 2.724 Cond. No. 12.2 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Sri K.


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Transcript

-
00:01 Hello student following is a dummy recreation variable result of mpgavg on cylindrical 4dump and cylindrical 6dump based on result solved for predicted mpgavg for 8 cylindrical cars.
00:22 So here equation is equal to intercept plus cyl 4dump into coefficient for cyl plus cyl 6dump into coefficient for cylindrical 6dump.
00:55 So here from the given output 6 .9545 plus 0 into 7 .2455 plus 0 into 3 .0758...
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