# Linear regression and correlation

4.6 Air Conditioning Repairs. Richard's Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job and let y denote the total cost to customer.

a) Obtain the equation that express y in terms of x

b) Find b0 and b.

c) Construct a table for the values x-values 0.5, 1, and 2.25. The table should be simple.

d) Calculate the cost exactly by using the equation from part (a).

*For examples 4.16 and 4.22 (see attached)

a) Find the y-intercept and slope.

b) Determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.

*For examples 4.24 and 4.30 (see attached)

a) determine whether it slopes upward, slopes downward, or is horizontal, without graphing the equation.

b) find its equation

4.44 Custom Homes. Hanna Properties specializes in custom-home resales in Equestrian Estates, an exclusive subdivision in Phoenix, Arizona. A random sample of nine custom homes currently listed for sale provided the attached information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand {see attachment for table}

a) Determine the regression equation for the data.

b) Describe in your own words the regression equation and the data points.

c) Describe the apparent relationship between square footage and price for custom homes in the Equestrian Estates.

d) What does the slope of the regression line represent in terms of size and price of custom homes in the Equestrian Estates?

e) Use the regression equation determine in part (a) to predict the price of a custom home in the Equestrian Estates that has 2600 sq. ft.

f) Identify the predictor and response variables.

g) Identify outliers and potential influential observations.

4.82 The linear correlation coefficient of a set of data points is 0.846.

a) Is the slope of the regression line positive or negative? Explain your answer.

b) Determine the coefficient of determination.

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#### Solution Summary

This solution is a Linear regression and correlation analysis on the data provided. Please see the attached Word document and Excel worksheet for solutions. The Word document shows all solultions with explanations. The Excel sheet shows the calculation details for finding the regression equation to predict a response variable (y) from an explanatory variable (x).