What is the purpose of multiple linear regression?

Sir Francis Galton, in the late 1800s, was the first to introduce the statistical concepts of regression and correlation. He studied the relationships between pairs of varlables such as the size of parents and the size of their affspring. Data similar to that which he studied are given below, with the variable x denoting the height (in centimeters) of a human father and the variable y denoting the height at maturity (in centimeters) of the father's oldest son. The data are given in tabular form and also displayed in the Figure 1 scatter plot. Also given is the product of the father's height and the son's helght for each of the fifteen pairs. (These products, written in the column labelled "xy", may aid in calculations.) Height of Height of son, father, x y (in centimeters) centimeters) xy (in 192.7 190.6 36,728.62 174.8 179.2 31,324.16 210 158.5 175.3 27,785.05 200 160.9 167.7 26,982.93 180- 171.6 182.0 31,231.2 172.2 171.1 29,463.42 170 179.9 187.9 33,803.21 181.5 177.5 32,216.25 130_…

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) through (c) below. Click the icon to view the data table. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y =x+O %D/ (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y = ý =x+O %3D (Round the x coefficient to three decimal places as needed. Round the constant to the nearest integer as needed.) (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance company use this information? What is the correct interpretation of the…

. A professor at the University of Alabama was interested in evaluating the relationship between family support and delinquency. Using data collected on 4545 families, the researcher used regression to analyze the relationship. The results are presented below.       Variables Entered/Removeda Model Variables Entered Variables Removed Method 1 Family supportb . Enter   a. Dependent Variable: Delinquency b. All requested variables entered.     Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .249a .062 .062 1.59168   a. Predictors: (Constant), Family support     ANOVAa Model Sum of Squares df Mean Square F Sig. 1 Regression 759.204 1 759.204 299.671 <.001b Residual 11479.107 4531 2.533     Total 12238.311 4532         a. Dependent Variable: Delinquency b. Predictors: (Constant), Family support…