Graphical Analysis In Exercises 11–14, determine whether there...

Question

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

Scatterplot showing a curved pattern of black dots, indicating no linear correlation between the x and y variables.

Accepted Answer

Hi everybody, Glad to have you back. Our next problem says a researcher studied the relationship between the number of hours employees spend in meetings per week and their productivity scores measured out of 100. The scattered plot below displays the data collected from 15 employees. Based on the scatter plot, how would you describe the linear correlation between meeting hours and productivity? So we have that plot, meeting hours versus productivity, productivity score on the Y axis, meeting hours on the X axis. And we can see we have a trend of dots. They adhere pretty closely to an imaginary straight line, and they're trending downwards and towards the left. Our answer choices are A, perfect positive linear correlation, B, strong positive linear correlation, C, strong negative linear correlation, or D, no linear correlation. So 2 of these we can rule out right away. Uh, they're definitely not a positive or perfect, excuse me, perfect linear correlation, so we can rule out choice A. Because our dots do not actually form a perfectly straight line, you can see that they wobble a little bit, for lack of a better word. And we can rule out choice D, no linear correlation, because we see that it is quite easy to draw an imaginary straight line, or dots are pretty close to that line. So, we know we have a strong correlation because, again, our dots are quite close to that imaginary line. Do we have a positive or negative linear correlation? Well, we see this downward to the left trend, which means that our variables are moving in opposite directions. As productivity and the Y axis decreases, we are increasing the X-axis or the number of hours. And moving in the opposite directions indicates a negative correlation. So choice C, strong negative correlation is our answer. If it were a positive linear correlation, we would see those dots that line of dots trending upward to the right. So, once again, in this case, we see that we have a choicey strong negative linear correlation. Since we have dots quite close to an imaginary straight line, that trend. Downward as you move to the right. See you in the next video.

Graphical Analysis In Exercises 11–14, determine whether there is a perfect positive linear correlation, a strong positive linear correlation, a perfect negative linear correlation, a strong negative linear correlation, or no linear correlation between the variables.

Key Concepts

Correlation

Scatterplot

Linear vs. Non-linear Relationships

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