Show the mathematical equation of this model. Please give two examples after you
ID: 3043921 • Letter: S
Question
Show the mathematical equation of this model. Please give two examples after you have the equation. Select any two meaningful numbers of X and predict the value
of Y and interpret the equation using words.
I think the equation will be: Y= 721956 + 460X, is that correct? And then I need help interpreting the equation using words & some ideas for two examples.
SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Squa Standard Error Observations 0.590441 0.348620574 0.335050169 11239.93247 50 ANOVA MS 1 32455448713245544871 25.68976988 Sign ITlcance Regression Residual Total 6.38139E-06 48 6064131929 126336081.9 49 9309676800 Coefficients Standard Errot Stat p-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept X Variable 1 72195.63069 2503.58649 28.83688305 5.72919E-32 -460.2643517 90.8086527-5.06850766 6.38139E-06 67161.83268 642.8473851 -277.6813183-642.8473851 77229.4287 67161.83268 77229.4287 -277.6813183Explanation / Answer
first of all look at the coefifcents of the intercept and the variables. then look for its p value .is it <0.05 or not ? if not then the given variable/intercept does not have any contribution in the regression equation.
In the current ANOVA table, there is an intercpet and only 1 variable. Also the p value of both is lower than 0.05 .Hence we shall consider it in our calculation.
the general linear regression equation is given by
y =mx+c
c=intercept coefficient , m=coefifcient of variable ,also known as slope.
Keeping values our linear regression equation becomes
Y=72195.6-460.2X
The intercept is nothing but the value that the dependent variable(Y) assumes when the independnent variable(X) is zero .
The slope /coefficient of variable is the rate of change of the dependent variable with respect ot change of the independent variable.It is the change in dependnent variable with a unit change in the independent variable.
Two examples
1).The relationship between the amount deposited in a bank on day zero (salary) and the expenditure per day. The bank deposit of a person depletes with passage of each day in a month.Let it deplete at the rate of 460$ per day and let initial bank deposit be $72195.
2). The relationship between total number of toys(Y) made in an industry with respect to taxation rate (X).If taxation rate is high ,the number of toys made will decrease and vice versa.
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