2. The production of wine is a? multibillion-dollar worldwide industry. In an at
ID: 3374995 • Letter: 2
Question
2. The production of wine is a? multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine? experts, data was collected from red wine variants of a certain type of wine. A sample of 12 wines is given. Develop a simple linear regression model to predict wine? quality, measured on a scale from 0? (very bad) to 10? (excellent), based on alcohol content? (%). Complete parts? (a) through? (d) below.
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Wine
Alcohol Content? (%)
Quality Rating
1
10.0
9
2
10.8
7
3
10.4
8
4
11.9
7
5
11.7
9
6
11.8
8
7
12.5
7
8
12.3
9
9
12.4
10
10
13.2
8
11
13.5
9
12
13.8
8
Click the icon to view the data of wine quality and alcohol content.
a. Construct a scatter plot. Choose the correct graph below.
A.A scatterplot with a horizontal axis labeled "Alcohol Content (%)" from 0 to 15 in increments of 5 and a vertical axis labeled "Wine Quality Rating" from 0 to 10 in increments of 2 contains 12 points. The coordinates of the points are as follows: (10, 9); (11, 7); (10, 8); (12, 7); (12, 9); (12, 8); (13, 7); (12, 9); (12, 10); (13, 8); (14, 9); (14, 8). All coordinates are approximate.
B.A scatterplot with a horizontal axis labeled "Alcohol Content (%)" from 0 to 10 in increments of 2 and a vertical axis labeled "Wine Quality Rating" from 0 to 15 in increments of 5 contains 12 points. The coordinates of the points are as follows: (9, 10); (7, 11); (8, 10); (7, 12); (9, 12); (8, 12); (7, 13); (9, 12); (10, 12); (8, 13); (9, 14); (8, 14). All coordinates are approximate.
C.A scatterplot with a horizontal axis labeled "Alcohol Content (%)" from 0 to 40 in increments of 5 and a vertical axis labeled "Wine Quality Rating" from 0 to 15 in increments of 5 contains 12 points. The coordinates of the points are as follows: (31, 10); (33, 11); (32, 10); (33, 12); (31, 12); (32, 12); (33, 13); (31, 12); (30, 12); (32, 13); (31, 14); (32, 14). All coordinates are approximate.
D.A scatterplot with a horizontal axis labeled "Alcohol Content (%)" from 0 to 15 in increments of 5 and a vertical axis labeled "Wine Quality Rating" from 0 to 40 in increments of 5 contains 12 points. The coordinates of the points are as follows: (10, 31); (11, 33); (10, 32); (12, 33); (12, 31); (12, 32); (13, 33); (12, 31); (12, 30); (13, 32); (14, 31); (14, 32). All coordinates are approximate.
b. For these? data, b0=7.5and b1=0.1 Interpret the meaning of the? slope, b1?, in this problem. Choose the correct answer below.
a.The? slope, b1?,implies that the alcohol content is equal to the value of b1?, in percentages.
b.The? slope, b1?, implies that for each increase of alcohol percentage of? 1.0, the wine quality rating is expected to increase by the value of b1.
c.The? slope, b1?, implies that for each 10.1 percentage decrease in alcohol? content, the wine should have an increase in its rating by 1.
d.The? slope, b1?, implies that for each increase of 1 wine quality? rating, the alcohol content is expected to increase by the value of b1?, in percentages.
c. Predict the mean wine quality for wines with an 3?% alcohol content.
^Yi=______________ (Round to two decimal places as? needed.)
d. What conclusion can you reach based on the results of? (a)-(c)?
a.Alcohol percentage appears to be affected by the wine quality. Each increase of 1 in quality leads to a mean increase in alcohol of about 0.1.
b.Wine quality appears to be affected by the alcohol percentage. Each increase of? 1% in alcohol leads to a mean increase in wine quality of about 0.1.
c.Alcohol percentage appears to be affected by the wine quality. Each increase of 1 in quality leads to a mean increase in alcohol of about 7.5.
d.Wine quality appears to be affected by the alcohol percentage. Each increase of? 1% in alcohol leads to a mean increase in wine quality of about 7.5.
Wine
Alcohol Content? (%)
Quality Rating
1
10.0
9
2
10.8
7
3
10.4
8
4
11.9
7
5
11.7
9
6
11.8
8
7
12.5
7
8
12.3
9
9
12.4
10
10
13.2
8
11
13.5
9
12
13.8
8
Explanation / Answer
a. The correct option would be A.
A.A scatterplot with a horizontal axis labeled "Alcohol Content (%)" from 0 to 15 in increments of 5 and a vertical axis labeled "Wine Quality Rating" from 0 to 10 in increments of 2 contains 12 points. The coordinates of the points are as follows: (10, 9); (11, 7); (10, 8); (12, 7); (12, 9); (12, 8); (13, 7); (12, 9); (12, 10); (13, 8); (14, 9); (14, 8). All coordinates are approximate.
b. The correct option is b.
b.The? slope, b1?, implies that for each increase of alcohol percentage of? 1.0, the wine quality rating is expected to increase by the value of b1.
c. yi=7.5+0.1x3= 7.8
d. The correct option is b.
b.Wine quality appears to be affected by the alcohol percentage. Each increase of? 1% in alcohol leads to a mean increase in wine quality of about 0.1.
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