Question

Asked May 7, 2019

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Step 1

**Note:**

Hey there! Thank you for posting the question. As the question you have posted has more than 3 parts, we have solved the first 3 parts for you. If you need help with any other part, please re-post the question and mention the parts you need solved.

You have not mentioned the sample size, which is necessary to find the confidence interval in part C. We have used trial-and error method to find the sample size and solved the problem using that sample size. However, if the sample size (*n*) we have obtained does not match with that in your original data, please replace the actual value of *n* in the formula we have provided, to get the answer. Henceforth, please mention the sample size in such problems.

Step 2

**Part A:**

Denote *y* as the response variable, median school API and *x* as the predictor, income. In the given output, the column “Parameter Estimate” gives the coefficient corresponding to the variable under the “Variable” column.

The ‘estimate’ of “Intercept” is the intercept of the regression model, which is 655.641. The coefficient of “Income” is the slope, which is given as 1.81123. Using these values, the equation for predicting *y* using *x* is: ** y = 655.641 + 1.81123 x**.

Step 3

**Part B:**

Three plots that can be used to determine whether the model assumptions are met are:

**Plot of residuals versus the fitted values:**The residuals (obtained by subtracting the predicted value using the equation from the observed value) are plotted against the fitted or predicted values of*y*. A random distribution of the plots suggests that the errors are indeed random in nature with respect to the response variable. It is not desirable to have a pattern of the residual plot.**Plot of residuals versus the predictor:**The residuals are plotted against the predictor variable values, that is, the values of*x*. Similar to the previous plot, a random distrib...

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