Verizon 7:27 PM c @ 30% (8 points) Question 4 The following table shows the outp
ID: 3326915 • Letter: V
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Verizon 7:27 PM c @ 30% (8 points) Question 4 The following table shows the output of a regression of selected S&P; 500 companies' net income in billions of dollars (the dependent variable) on their sales in billions of dollars (the independent variable). SUMMARY OUTPUT ression Stotistics Multiple R Square Adjusted R Square Standard Enror Observations 0.726492486 0.526571154 1444.608669 1 $02692213.7 9026922137 432.5529349 49O34E-65 387 807628057.7 2086894.206 Residual ents Stondord Error Sales 0.062578367 0.003008878 20.79790698 490343- 005662574 0.068494161 Part (a) Interpret the estimated value of the slope coefficient, i.e., explain what the number means in this regression. (2 points) Part (b) (2 points) Interpret the estimated value of the intercept, i.e., explain what the number means in this regression. Part (c) Does the estimated value of the intercept make sense? Why or why not? (2 points) Part (d) (2 points) Is the estimate of the slope coefficient statistically significant? Please answer "yes" or "no" and explain how you can tellExplanation / Answer
For simple linear regression, which is represented by the equation of theregression line: = b0 + b1x, where b0 is a constant, b1 is the slope ( regression coefficient), x is the value of the independent input variable, and is the predicted value of the dependent output variable.
In other words, Slope is the ratio of Rise and Run on the regression line for two corresponding values of y and x i.e. (y2-y1)/ (x2-x1). What this means is, The slope of a regression line (b1) represents the rate of change in y as x changes. Because y is dependent on x, the slope describes the predicted values of y given x.
Mathematically, Slope is also understood as the tangent of the angle that the regression line makes with the X-axis.
The intercept (often labeled the constant) is the expected mean value of Y when all X=0.
If X never = 0, then the intercept has no intrinsic meaning. In scientific research, the purpose of a regression model is to understand the relationship between predictors and the response. If so, and if X never = 0, there is no interest in the intercept. It doesn’t tell you anything about the relationship between X and Y.
c
Clearly this constant is meaningless and you shouldn’t even try to give it meaning. zero sale cant generate any income, its just a best fitted curve.
d
If the p-value for a variable is less than your significance level, your sample data provide enough evidence to reject the null hypothesis for the entire population. Your data favor the hypothesis that there is a non-zero correlation. Changes in the independent variable are associated with changes in the response at the population level. This variable is statistically significant and probably a worthwhile addition to your regression model.
On the other hand, a p-value that is greater than the significance level indicates that there is insufficient evidence in your sample to conclude that a non-zero correlation exists.
as p value is 4.9...E-65, it does make sense that income is related to sales.
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