Use the following data for parts (a) through (f). x 5 7 3 16 12 9 y 8 9 11 27 15

Question

Use the following data for parts (a) through (f).

x 5 7 3 16 12 9

y 8 9 11 27 15 13

Determine the equation of the least squares regression line to predict y by x.

Using the x values, solve for the predicted values of y and the residuals to answer the next question.

Solve for se.

Solve for r2.

Test the slope of the regression line. Use =.01.

Comment on the results determined in parts (b) through (e), and make a statement about the fit of the line.

Answers:

(a) y^= +(__________ )x [Round to 4 decimal places, the tolerance is +/- 0.0005]

(b) Fill in the blanks. (Round your answers to 3 decimal places.)

x y (yy^) residuals

3 _______ ________

5 __________ __________

7 ________ _________

9 ___________ ___________

12 __________ _____________

16 ___________ ____________

(c) se= ________(Round your answer to 3 decimal places.)

(d) r2= _________ (Round to 3 decimal places.)

(e) The decision is ____________the null hypothesis.

(f) The slope of the regression line___________ different from zero using = .01. However, for = .05, the null hypothesis of a zero slope is _____________.

Explanation / Answer

a] The regression equation is Y = 2.69 + 1.29 X

b] x      Y-hat      (Y-Y-hat)

     3       6.550        4.450

     5       9.121      -1.121

     7       11.691     -2.691

     9      14.262      -1.262

    12    18.118      -3.118

    16     23.259      3.741

c]

se = 3.661

d] r^2 = 0.777

e] here = 0.01 and p-value = 0.02, P-value is greater than = 0.01. Hence we failed to reject null hypothesis.

f] The slope of the regression line 1.285 is different from zero using = 0.01. However for for = .05, the null hypothesis of a zero slope is accept null hypothesis. Because p-value = 0.02 is less than = 0.05.

that is the slope of the regression line is zero.

Using MINITAB follow the following procedure

Choose Stat > Regression > Regression.

In Response, enter Score2.

In Predictors, enter Score1.

Click OK.

Session window output

MTB > Regress 'Y' 1 'X';
SUBC>   Constant;
SUBC>   Brief 1.

Regression Analysis: Y versus X

The regression equation is
Y = 2.69 + 1.29 X

Predictor    Coef    SE Coef     T      P
Constant    2.694    3.334 0.81 0.464
X           1.2853   0.3439 3.74 0.020

S = 3.66090   R-Sq = 77.7%   R-Sq(adj) = 72.2%
Analysis of Variance

Source         DF      SS      MS      F      P
Regression         1 187.22 187.22 13.97 0.020
Residual Error      4   53.61   13.40
Total         5   240.83

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.