If you regress daily high temperature y on the amount of ice...

If you regress daily high temperature (Y) on the amount of ice cream sales (X), you will notice that there is a strong positive correlation between the two. In other words, as daily ice cream sales increase, the daily high temperature increases. This implies that if we knew the amount of ice cream sales in a particular day, we could estimate, with a high level of accuracy, the high temperature in that day. Does this mean that if we wanted to increase the daily temperature, we need to sell more ice cream? Explain why or why not?

Transcript

00:01 Now in this video, we've actually been given a graph, which was the relationship between ice cream sales and then weather.

00:11 Now, it's quite unfortunate the graph could not appear in this question.

00:16 However, we were giving persons correlation coefficient, persons correlation coefficient to be 0 .80 with p value.

00:30 Less than 0 .01.

00:34 Now, we're asked, first of all, what is the direction? a.

00:40 So we're going to find the direction of this person's correlation coefficient.

00:46 Now, person correlation coefficient could be positive as in this case, or negative.

00:53 If it is positive, as we have in this case, then the direction is what is increasing or is a direct there is direct impact okay so this one we can say the direction is such that so let's try to write something small the direction is what is such that as the weather increases or as temperature increases as temperature as temperature increases then then sales also increase okay so it's a positive direction as temperature increases then sales of ice cream also ice cream also increase also increase or in other ways ways you can say it is in the positive direction direction is in the positive positive or direct impact impact okay so that is what we can say to for the direction of the of the of the of the person correct coefficient of 0 .80.

02:48 Now the next thing we are asked to do, which is question b, we are asked what does p value less than 0 .01 mean? what does it mean? what does it mean? now we normally compare p value with significant levels and because we're not giving the scriptural level in this study, the standard statistics level that we use is 0 .05 and p value of 0 .01 means that our test is statistically significant.

03:28 Okay, our test or whatever relationships we found between sales of ice cream and the temperature.

03:39 So we can just write our test or finding is statistically statistically significant significant that's the next thing we can see then our last question is what is the direction or what is the strength of the person correlation coefficient what is a strength so correlation coefficient actually ranges between zero negative one less than or to correlation coefficient and one this is the range for it okay now if it is close to zero or zero itself then we can say there is no correlation however 0 .80 we can say there is a strong positive correlation so this one simply means or the strength is what strong positive correlation or we can even say strong direct correlation strong direct of strong direct of strong direct correlation strong direct correlation okay strong and then direct correlation that is what we can say is the strength of our it is strong it is not intermediate it is not weak by a strong and direct correlation.

05:34 All right, because correlation from 0 .75 up to one in both directions, whether positive or negative, we say they are strong correlations.

05:50 Okay.

05:51 All right.

05:52 So this is a strong and a direct correlation...

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