Answer to this questions plz?? Refer to the scatterplot on the right, where the

Question

Answer to this questions plz?? Refer to the scatterplot on the right, where the diameter of ball 1 is the independent variable and the diameter of ball 2 is the dependent variable. 25.0 a. Would it make sense to find the this data set? N Why or correlation with why not? 17, ALLM b. Would the correlation be positive, negative, or near o? 15, 15.0 17.5 20.0 22.5 25.0 Ball 1 (cm) C Book o A. No, because there is a nonlinear trend in the data O B. Yes, because there is a linear trend in the data. STU O c. No, because there are not enough data points in the scatterplot. (o) TUTO O D. No, because there is no trend in the data b. Choose the correct answer below. O Near zero O Negative O Positive Click to select your answer.

Explanation / Answer

First Problem (Image 1):

(a) The response variable or the dependent variable (Y) is diameter of Ball 2.

The predictor variable or the independent variable (X) is diameter of Ball 1.

From the scatterplot, we can see that there is a linear trend in the data. In fact there exists a negative linear relationship between X and Y.

Therefore, it would make sense to find the correlation with this data set, as there is a linear trend in the data.

So, the correct option is B. Yes, because there is a linear trend in the data.

(b) From the scatterplot, we can see that there exists a negative linear relationship between X and Y. This is because, if we draw a trend line (also called regression line), the slope will be negative.

In other words, we can say that as X increases, the value of Y decreases. Therefore, the correlation will be negative. So, the correct option is Negative.

Second Problem (Image 2):

(a) 0.02

This is because there does not exists any linear relationship between dependent and independent variables. Hence the correlation coefficient will be near zero.

(b) 0.63

This is because there exists a week positive linear relationship between dependent and independent variables.

(c) - 0.93

This is because there exists a strong negative linear relationship between dependent and independent variables.

Third Problem (Image 3)

It is given that growth rate of a children looks like a straight line. Therefore, we must not predict outside the ranges of the data. In other words, if we want to predict the height of the child at 21 years using this model, there would be error. Also note that the normal growth rates slow down as people get older.

Therefore the correct option is D.

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