問15
頻出度★★★
気温と売上高の関係が負の相関となっているものはどれか。
平成23年度 特別試験 ITパスポート試験 問15
ストラテジ系企業活動 › 業務分析・データ利活用
This question's explanation and your answers so far.
解説
問 15
Incorrectア
The points form a band that rises to the right, going up from the lower left to the upper right. On the left side where the temperature is low, sales are low, and the higher the temperature, the higher the sales; this is a relationship in which one increases as the other increases, that is, a positive correlation. Sales of products that sell better the hotter it gets, such as beer, ice cream, and soft drinks, form this shape. The correlation itself can be read clearly, but its direction is the opposite, and it is not the negative correlation the question asks for, so it is wrong.
- イ
正解 The correct answer is イ. A scatter plot is a graph for looking at the relationship between two kinds of data; here temperature is on the horizontal axis and sales on the vertical axis, and each day's result is plotted as a single point. When the spread of the points shows a slope that rises to the right or falls to the right, the two kinds of data are said to be correlated. Among these, a relationship in which one value gets smaller as the other gets larger is called a negative correlation (inverse correlation), and on a scatter plot it appears as a band of points falling to the right, running from the upper left down to the lower right. The scatter plot in イ has exactly this shape: on the left side where the temperature is low, the points gather near the top (high sales), and as the temperature rises and you move to the right, the position of the points steps down, reaching its lowest at the far right end. The points also stay together in a band with little scatter, so the slope can be read clearly, which makes it a strong negative correlation. A familiar example is products that stop selling as the temperature rises, such as oden, hot canned drinks, and heating appliances; their sales form this shape. Of the other three, ア rises to the right (positive correlation), ウ is flat (no correlation), and エ is scattered about (no correlation), so イ is the only one that shows a falling-to-the-right trend. Therefore, the one in which temperature and sales are negatively correlated is イ.
Incorrectウ
The points line up in a long, narrow band running sideways at roughly the same height, neither rising nor falling. In other words, whether the temperature is low or high, sales stay almost constant, and changes in temperature are not linked to increases or decreases in sales. A state like this, where the arrangement of the points can be read as neither rising to the right nor falling to the right, is called no correlation (uncorrelated), and it is not a negative correlation, so it is wrong. Sales of everyday goods whose sales are not easily swayed by temperature or season form this shape.
Incorrectエ
The points are scattered irregularly up, down, left, and right, with high-sales points and low-sales points mixed together in the same temperature range, so no consistent slope can be found overall. This is also no correlation; the only difference from ウ is that sales vary more widely (they are spread out over a wide vertical range), and it is the same in that there is no regular increase-or-decrease relationship with temperature. A wide spread by itself does not mean a negative correlation, so it is wrong. To judge something as a negative correlation, you must be able to read a consistent slope that goes down as you move to the right.
ここがポイント
- Reading correlation from a scatter plot — A scatter plot is a graph that expresses the relationship between two kinds of data through the spread of the points. If the points line up from the lower left to the upper right and rise to the right, it is a positive correlation (one increases as the other increases); if they line up from the upper left to the lower right and fall to the right, it is a negative correlation (one decreases as the other increases); if they are flat or scattered so that no slope can be read, it is no correlation (uncorrelated). The first step in solving such a question is to look at the direction in which the points line up and judge whether the correlation is positive, negative, or absent.
- The strength of a correlation, and the difference between correlation and causation — The more the points come together into a thin, straight line, the stronger the correlation; the more thickly they scatter, the weaker it is. However, the existence of a correlation does not mean there is a causal relationship. As with temperature and sales, a third factor (such as the season) may be affecting both, so in data analysis you must separate the question of whether a correlation exists from the task of identifying the cause.
用語