Use a linear regression equation to make a prediction about paired data when app

Question

Use a linear regression equation to make a prediction about paired data when appropriate AND identify a situation in which it is not appropriate.

Use a linear regression equation to make a prediction about p appropriate AND identify a situation in which it is aot appropriate aired data when o Four scatter plots are given below, along with the regression equation. Match each scatter plot with the corresponding correlation coefficiens (no calculatioms ane necessary for thisl) a y-0.63x+22.24 b·9-0.64x + 12.32 y=0.29x+1.76 -1.53x+78.16 c. Match these values with the scatter plots above (not all will be used): r=0.260 For each scatter plot above, either use the regression equation to predict the value r=0 r=-0.962 r=0.868 r=-0.147 rel of y which corresponds to x-35, or explain why it is not appropriate to do so. Suppose IQ scores were obtained from randomly selected couples. For 20 such pairs of people, the linear correlation coefficient is 0.897 and the equation of the regression line is ý -2.05+1.04x, where x represents the 1Q score of the husbund. Also, the 20 x values have a mean of 100.88 and the 20 y values have a mean of 102.7. What is the best predicted 1Q of a randomly selected wife, given that her husband has an leQ o of 94?

Explanation / Answer

Question

(i) For first scatter plot (a) : r = -1 (all points are on line)

(ii) for second scatter plot (b) : r = 0.868 ( as r must be positive and residuals are very closely fitted to regression line)

(iii) for third scatter plot (c) : r = 0.260 ( as r must be positive and residuals are arbitrely scattered and not closely fitted)

(iv) For fourth scatter plot (d) : r = -0.962 ( as r must be negative and residuals are tightly associated with the regression line)

Question 2

IQ of the husband = 94

So as per the predicted line

y^ = -2.05 + 1.04 x

so here x = 94

so IQ of the wife y^ = -2.05 + 1.04 * 94 = 95.71

Question 3

Height of the women = 67 inch

y^ = 18.4 + 0.860 x

y^(67 inch) = 18.4 + 0.86 * 67 = 76.02

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