(a) Find an equation of the least squares regression line. Please show all work.

Question

(a) Find an equation of the least squares regression line. Please show all work.

(b) Based on the equation from part (a), what is the predicted value of y if x = 2? Show all work and justify your answer.

True or False.

1. (a) If the variance of a data set is zero, then all the observations in this data set are zero.

(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.

(c) Assume X follows a continuous distribution which is symmetric about 0. If , then .

(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.

(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .

Please show all work work and give justification for #1. Please no handwritten work.

Explanation / Answer

Slope(b) = (NXY - (X)(Y)) / (NX2- (X)2)

b = (4 * 57 - 9*16) / (4*35 - 92)

b = 1.424

Intercept(a) = (Y - b(X)) / N

a = (16 - 1.424*9) / 4 = 0.797

Equation: Y = 1.424X + 0.797

b) X = 2

Y = 1.424*2 + 0.797 = 3.644

For X = 1; Y = 2

For X = 3, Y = 5

Hence for X = 2 Y has to be 2 < Y < 5

Y = 3.644 and hence is justified

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a) If the variance of a data set is zero, then all the observations in this data set are zero - TRUE

b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9 - FALSE

If two events are disjoint, then the probability of them both occurring at the same time is 0. Disjoint: P(A and B) = 0.

c) Assume X follows a continuous distribution which is symmetric about 0. If , then - standard normal distribution

d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter. - FALSE

Since margin of error is high

e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance - FALSE

P(t > 1.5) = 1 - 0.96 = 0.04 which is less than alpha (0.05) - Reject the NULL

X Y X2 Y2 XY 0 1 0 1 0 1 2 1 4 2 3 5 9 25 15 5 8 25 64 40 Sum X = 9 Sum Y = 16 Sum X2 = 35 Sum Y2 = 94 Sum XY = 57

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