Scatterplot Diagrams Statistics Questions

Part 1

Question 1

A scatterplot is, in essence, a graph that is used to denote how two quantitative variables relate. When the two variables being measured increase, i.e. an increase in workforce motivation as a consequence of an increase in benefits, this is referred to as positive correlation. On the other hand, when one variable increases as the other decreases, i.e. performance of students decreasing as classroom attendance decreases, this is referred to as negative correlation.

Question 2

Scatterplot

Relationship: There is a positive correlation between R&D and sales

Question 3

A good example of two pairs of variables that are positively correlated would be the time spent on the treadmill versus calories burnt. In essence, the more minutes a person spends on the treadmill, the more calories such a person burns (Peyman, 2017). This is an exercise that involves various body muscles, thus burning more calories than would be the case if an individual failed to engage in any body activity.

Question 4

A pair of variables showing strong positive correlation would NOT necessarily mean that one variable is a cause for the other. The strongest positive correlation is denoted by 1. This in essence means that an increase in one variable is accompanies by a certain increase in the other. However, it is important to note that this correlation does not indicate or guarantee causation. In the words of Steinberg (2010), “a correlation coefficient, no matter how high, does not indicate where the cause lies” (p. 452). The cause of movement could be triggered by a myriad of other factors. For instance, while there could be strong correlation between student performance and class attendance, the said attendance could also be brought about by a change in instructional strategies, change in student attitudes about education, etc.

Question 5

With regard to correlation measure r,

d) r is always between -1 and 1

Question 6

a) x and y have a strong positive correlation = 1

b) x and y are not correlated = 0

c) x and y show mild negative correlation -0.1

Question 7

a) By definition, “a regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes” (Peck and Devore, 2011). In that regard, therefore, it comes in handy in seeking to determine ‘y’ value for every assigned ‘x’ value.

b) For a regression line to be used, there ought to be a linear relationship between two variables

c) Regression analysis comes in handy in seeking to determine what relationships exist among data. This is particularly important given that it is often difficult to derive any meaningful trends or associations when looking at raw data visually. In addition to helping in the determination of “standard error of estimate to measure the variability or spread of values of a dependent variable around a regression line,” regression analysis also “helps in developing an algebraic equation between two variables based on the given data and estimating the value of a dependent variable given the value of an independent variable” (Sharma, 2010, p. 408).

Question 8

Two components of a one variable regression equation:

i) One input variable (x)

ii) One output (y)

Question 9

a) A residual is “the difference between an observed value of dependent variable y and its estimated (or fixed) value for a given value of the independent variable x” (Sharma, 2010, p. 431).

b) If I were to connect the scatter plot points to the regression points, the vertical distance between the said points would be the residual.

Part 2

a),

b)

Correlation for the two variables = -0.96912

c) If the weight of the vehicle is 32, the gas mileage will be -0.4435(32) + 32.397

= 46.589 miles per gallon

d) For vehicles that weigh more than 3200 pounds, there should be a gasoline surcharge. This is more so the case given that the relationship denoted between the two variables is strong negative correlation. This means an increase in weight leads to a decrease in miles covered.