Question

Can you please help me solve this problem and show steps? Thank you!

You have uncovered some information about the relationship of gun sales to target sales. The following table contains the average dollar volume in thousands of guns sold and the average dollar number in thousands of targets sold for a large sporting goods store. Table 4: Gun Sales and Target Sales Year Gun Sales Target Sales 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 3100 4500 5500 6125 7500 7800 9200 10100 8577 9430 10520 11600 250 270 367 400 512 533 620 673 625 613 700 733 Calculate the relationship of guns sold to targets sold. Allow the targets to be the dependent variable. What is the best fit equation? For each dollar in guns sold, how much will be generated in target sales. Comment on the Pearson coefficient value and the relationship to confidence.

Answer 1

The relationship between the two variables is determined as under:

Simple Linear Regression (Least Squares Regression Method 7750009610000 62500 2025000072900 2018500 30250000 134689 2450000 37515625 160000 3840000 56250000 262144 4157400 60840000 284089 5704000 84640000 384400 6797300 102010000 452929 5360625 73564929 390625 5780590 88924900 375769 7364000 110670400 490000 8502800 134560000 537289 93952 6296 53965215 809085854 3607334 3100 4500 5500 6125 7500 7800 9200 10100 8577 9430 10520 11600 250 270 367 400 512 533 620 673 625 613 700 733 Regression Equation: y a bx, where x- Gun Sales (independent variable) y Target Sales (dependent variable) a intercept point of regression line and y-axis b slope of regression line 12 93952 6296 Ex2-809085854 (Ех)"- Exy = | 8826978304 53965215 39639616 3607334| (Еу- ΣΥ- Slope (b) - N Ex - (Ex) Intercept (a) Regression Equation: y 26.7211 + 0.0636x Pearson correlation, r- r0.9882

The best fit equation is: y = 26.7211 + 0.0636*x

For each dollar in guns sold, target sales = 0.0636

Pearson coefficient (r) = 0.9882

This is positive number very close to 1. It indicates very strong positive correlation between the two variables.

Coefficient of determination, r2 = 0.9882^2 = 0.9766

It means that the the independent variable (Gun Sales) explains 97.66 % of the variation in target sales.