Question

8 11. Use the following table to answer the questions Х Y 7 18 23 10 28 13 32 14 37 16 41 20 45 26 52 a. Make a scatterplot and determine the relationship between X and Y b. Find the linear regression equation Y' =(round a and b to the nearest hundredth ) c. Find r and to the nearest hundredth d. Use the equation found in part b to determine X to the nearest whole number when Y' - 60

Answer 1

Question (a)

The scatterplot is as follows

The relationship between X and Y is positive linear relationship

х Y 18 7 8 Scatterplot with X on X-axis and Y on Y-axis 23 28 60 10 y = 1.7478x + 9.5937 R? = 0.9501 13 32 50 14 37 16 41 40 20 45 30 26 52 20 10 0 0 un 10 15 20 25 30

Question (b)

The regression output is as follows

Y SUMMARY OUTPUT х 7 IT 18 8 23 10 28 13 32 Regression Statistics Multiple R 0.9747 R Square 0.9501 Adjusted R Square 0.9417 Standard Error 2.7641 Observations 8 14 37 16 41 20 45 26 52 ANOVA df SS MS F Significance F 0.0000 1 114.1508 Regression Residual Total 872.1576 45.8424 918.0000 872.1576 7.6404 6 7 Coefficients Standard Error t Stat P-value Lower 95% 9.5937 2.5277 3.7954 0.0090 3.4086 Intercept X Variable 1 Upper 95% 15.7788 2.1481 1.7478 0.1636 10.6841 0.0000 1.3475

The linear regression equation is

Y' = 1.7478 * x + 9.5937

Y' = 1.75 * x + 9.59 rounded to nearest hundreth

Question (c)

r value is the Multiple R value from the Regression statistics section in the above output

So r = 0.9747

= 0.97 rounded to nearest hundreth

r² value is the R square value from the Regression statistics section in the above output

So r² = 0.9501

= 0.95 rounded to nearest hundreth

Quesion (d)

Given Y' = 60

Y' = 1.7478 * x + 9.5937

60 = 1.7478 * x + 9.5937

1.7478 * x = 60 - 9.5937

1.7478 * x = 50.4063

x = 50.4063 / 1.7478

= 28.9399

= 29.94 rounded to nearest hundreth