Math 54+54C Section 4.1, 4.2
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Math 54+54C
Section 4.1, 4.2
1. The data set below gives the weight of a car, in pounds, and its fuel rating, in miles per gallon.
|
Weight |
4724 |
4006 |
3097 |
3555 |
4029 |
3934 |
3242 |
2960 |
3530 |
3823 |
|
MPG |
17 |
18 |
22 |
19 |
19 |
19 |
24 |
26 |
19 |
18 |
a. Determine which variable is the explanatory and which is the response variable. Explanatory__________________ Response______________________
a. Draw a scatter diagram of the data set.
b. Compute the linear correlation coefficient, r, between the two variables. Round to three decimal places.
r = ___________
2. The data below are the number of absences and the final grades of 9 randomly selected students from a literature class. Find the equation of the regression line for the given data.
|
Number of absences, x |
0 |
3 |
6 |
4 |
9 |
2 |
15 |
8 |
5 |
|
Final grade, y |
98 |
86 |
80 |
82 |
71 |
92 |
55 |
76 |
82 |
a) Determine whether or not there is linear relation between the number of absences and the final grades. If the relation is linear, determine the direction of the linear relation.
b) Find the equation of the least-square regression line. Round the regression line values to the nearest hundredth.
c) What would be the predicted final grade if a student was absent 14 times?
Is this a reasonable question? Round the predicted score to the nearest whole number.
3. A residual is the difference between _______________ and ________________.
4. To investigate the relationship between yield of soybeans and the amount of fertilizer used, a researcher divides a field into eight plots of equal size and applies a different amount of fertilizer to each plot. The table shows the yield of soybeans and the amount of fertilizer used for each plot.
|
Amount of fertilizer (pounds), x |
1 |
1.5 |
2 |
2.5 |
3 |
3.5 |
4 |
4.5 |
|
Yield of soybeans (pounds), y |
25 |
21 |
27 |
28 |
36 |
35 |
32 |
34 |
Compute the linear correlation coefficient between the two variables and determine whether a linear relation exists.
5. The data below shows the relationship between the number of years that employees have studied a particular language and the grades they received on the proficiency exam. Find the equation of the regression line for the given data. Round the regression line values to the nearest hundredth.
|
Number of absences, x |
3 |
4 |
4 |
5 |
3 |
6 |
2 |
7 |
3 |
|
Final grade, y |
61 |
68 |
75 |
82 |
73 |
90 |
58 |
93 |
72 |
a) Determine whether or not there is linear relation between the number of absences and the final grades. If the relation is linear, determine the direction of the linear relation.
b) Find the equation of the least-square regression line. Round the regression line values to the nearest hundredth.
2022-05-21