Chapter 27, Problem 38E

a)

To determine

To fit the regression model.

Answer to Problem 38E

  $TotalMidterm=46.0619+1.5801\times Homework$

Explanation of Solution

Given:

Midterm 1	Midterm 2	Homework	Total Midterm
82	30	61	112
96	68	72	164
57	82	69	139
89	92	84	181
88	86	84	174
93	81	71	174
90	83	79	173
83	21	51	104
59	62	58	121
89	57	79	146
83	86	78	169
95	75	77	170
81	66	66	147
86	63	74	149
81	86	76	167
81	87	75	168
98	96	84	194
50	27	20	77
91	83	71	174
87	89	85	176
90	91	68	181
95	82	68	177
91	37	54	128
93	81	82	174
88	66	82	154
99	90	77	189
89	92	68	181
87	62	72	149
92	66	78	158
62	43	56	105
93	87	80	180
95	93	87	188
93	65	66	158
92	98	77	190
91	95	83	186
92	80	82	172
61	58	65	119
55	65	51	120
76	88	67	164
63	62	67	125
89	66	72	155
91	42	66	133
90	85	78	175
75	62	72	137
75	46	72	121
91	65	77	156
84	70	70	154
94	92	81	186
93	78	72	171
91	58	66	149
91	61	79	152
89	86	62	175
98	92	83	190
96	51	83	147
95	95	87	190
98	89	77	187
89	79	44	168
93	89	73	182
74	64	72	138
97	96	80	193
94	90	88	184
81	89	62	170
94	85	76	179
92	90	86	182

Using excel,

  

The general regression equation is,

  $\widehat{y}=b_0+b_{1}x$

Here,

  $\begin{array}{l}{b}_0=46.0619\\ b_1=1.5801\end{array}$

Therefore, the equation of regression line is,

  $TotalMidterm=46.0619+1.5801\times Homework$

b)

To determine

To check the assumptions and conditions for inference.

Answer to Problem 38E

All conditions satisfied.

Explanation of Solution

Given:

  

  

  

The conditions are: straight enough, Independence, Constant variance and Normal residual.

We will check it one by one.

Straight enough condition: Satisfied, because no curvature is present in the scatterplot.

Independence assumption: Satisfied, because there is no obvious pattern in the residual plot.

Constant variance: Satisfied, because the vertical spread in the residual plot is not increasing or decreasing.

Random residuals condition: Satisfied, because there is no obvious pattern in the residual plot.

Nearly normal condition: Satisfied, because the pattern in the normal probability plot of residual is roughly linear.

Hence, all the conditions satisfied.

Now, p-value corresponding to coefficient is zero. It indicates that there is sufficient evidence that the slope is non-zero. The value of R-square is 0.507 indicate that the relationship is moderate.

c)

To determine

To explain whether she can accurately judge a student’s performance without giving the midterms.

Answer to Problem 38E

Not very accurate.

Explanation of Solution

Given:

  

The value of R-square is 0.507 indicate that the relationship is moderate. Also, standard error of the estimate se = 18.3043 which is very large. Hence, the predictions are not very accurate.