Question

JDL. Assume the data set has a bell- 42 The mean score of a competency test is 82, with a standard deviation of 2,Between what two values do abou+99.7% of the values lie? (Assume the data set has a bell-shaped distribution.) *For paired data sets 5 -3 -10-8 -2 2 -6 43.(5 pts) Find the equation of the regression line for the given data .一(4-1,l$2-c4 Use the regression equation to predict the value of y for x 2 45. Find r and explain the type of relation between x and y 46. What percentage of variability of the dependent variable is explained by the regression line?

Can someone please help me with the working out of problems 43 to 46. i want to know how to arrive at the correct answer. thanks.

Answer 1

There is two dataset X & Y

X= (-5,-3,4,1,-1,-2) & Y= (-10,-8 ,9 ,1 ,-2 ,-6)

43) Regression line for Y on X is

Y=2.1800*X - 0.4867

44 ) At X=2.2, Y= 4.309476

45 ) The correlation coffient between x & y is  0.9881905. Means these two vector x & y are highly correlated i.e. there is a strong relationship between x & y.

46) Since R square= 0.9765 ~ 100%. Thus 97.65% of variation in dependent variable y explained by regression line.

I am attaching my R-code for the detail solution of above problem.

> x=c(-5,-3,4,1,-1,-2)
> y=c(-10,-8,9,1,-2,-6)
> lm(y~x)
> predict(model, newdata=data.frame(x=2.2))
> cor(x,y)
> summary(lm(y~x))