Question

Complete parts​ (a) through​ (c) using the following data.

Row 1 1 2 2 2 2 2 6 6 6 8

Row 2 94 85 86 71 94 65 74 87 60 62

​(a) Find the equation of the regression line for the given​ data, letting Row 1 represent the​x-values and Row 2 the​ y-values. Sketch a scatter plot of the data and draw the regression line.

Input the values of the slope and intercept for the regression line when Row 1 represents the​ x-values.

.

y =_____ x+ ( __ , __ ) (Round to three decimal places as​ needed.)

​(b) Find the equation of the regression line for the given​ data, letting Row 2 represent the​ x-values and Row 1 the​ y-values. Sketch a scatter plot of the data and draw the regression line.

c) Construct a residual plot.

​(d) Determine if there are any patterns in the residual plot and explain what they suggest about the relationship between the variables. Choose the best answer in the parenthesis.

The residual plot (shows, or does not show ) a pattern because the residuals ( fluctuate or ,do not fluctuate)about 0. This implies the regression line ( is or is not)

a good representation of the relationship between the variables.

Answer 1

We use Minitab to solve this question.

MTB > Regress;
SUBC>   Response 'Row2';
SUBC>   Nodefault;
SUBC>   Continuous 'Row1';
SUBC>   Terms Row1;
SUBC>   Constant;
SUBC>   Unstandardized;
SUBC>   Tmethod;
SUBC>   Tanova;
SUBC>   Tcoefficients;
SUBC>   Tequation.

Regression Analysis: Row2 versus Row1

Analysis of Variance

Source         DF Adj SS Adj MS F-Value P-Value
Regression      1   459.8 459.76     3.47    0.099
Row1          1   459.8 459.76     3.47    0.099
Error           8 1059.8 132.48
Lack-of-Fit   2   132.4   66.19     0.43    0.670
Pure Error    6   927.5 154.58
Total           9 1519.6

Coefficients

Term       Coef SE Coef T-Value P-Value   VIF
Constant 88.39     6.75    13.09    0.000
Row1      -2.86     1.54    -1.86    0.099 1.00

Regression Equation

Row2 = 88.390 - 2.860 Row1

MTB > Regress;
SUBC>   Response 'Row1';
SUBC>   Nodefault;
SUBC>   Continuous 'Row2';
SUBC>   Terms Row2;
SUBC>   Constant;
SUBC>   Unstandardized;
SUBC>   Gnormal;
SUBC>   Gfits;
SUBC>   Gorder;
SUBC>   Tmethod;
SUBC>   Tanova;
SUBC>   Tcoefficients;
SUBC>   Tequation.

Regression Analysis: Row1 versus Row2

Analysis of Variance

Source         DF   Adj SS   Adj MS F-Value P-Value
Regression      1 16.9731 16.9731     3.47    0.099
Row2          1 16.9731 16.9731     3.47    0.099
Error           8 39.1269   4.8909
Lack-of-Fit   7 38.6269   5.5181    11.04    0.228
Pure Error    1   0.5000   0.5000
Total           9 56.1000

Coefficients

Term         Coef SE Coef T-Value P-Value   VIF
Constant    11.92     4.47     2.67    0.028
Row2      -0.1057   0.0567    -1.86    0.099 1.00

Regression Equation

Row1 = 11.920 - 0.106 Row2

Normplot of Residuals for Row1

Residuals vs Fits for Row1

Residuals vs Order for Row1

MTB > Plot 'Row1'*'Row2';
SUBC>   Symbol;
SUBC>   Regress.

Scatterplot of Row1 vs Row2

MTB > Plot 'Row2'*'Row1';
SUBC>   Symbol;
SUBC>   Regress.

Scatterplot of Row2 vs Row1

d)

The residual plot shows a pattern because the residuals fluctuate about 0 this implies the regression line is a good representation of the relationship between the variables.