Question

11. Use the following table to answer the questions X Y 7 18 8 23 10 28 13 32 37 16 41 20 45 52 14 26 a. Make a scatterplot and determine the relationship between X and Y b. Find the linear regression equation Y' = (round a and b to the nearest hundredth ) c. Find r and r’ to the nearest hundredth d. Use the equation found in part b to determine X to the nearest whole number when Y' = 60 12. Using a normal distribution and z score formula answer the following questions: a. Find the Z-score that cuts off the top 35% of the nornval curve b. Find the data value to the nearest whole number that cuts off the bottom 20% of the curve given that the mean is 75 and sample standard deviation is 5. c. Find the z scores that cut off the middle 50% of the normal curve.

Answer 1

11. (a) just simply plot values of x on x axis and corresponding y values on y axis . The resulting graph is scatter plot.

It will look like this :

(b) to find linear regression equation : Y = a + bX

52 其 50- 48 46 其 44 42- 载 40- 38 其 36- 94- 321 基 30- 2色 26 24 基 22- 20- 184 6 10 12 14 16 18 20 22 24 26

( Y and X are given , we need to find a and b )

Use the normal regression coefficients formula given below:

α = Σν)Σx)- (Σκ)Σxy) n (Σx2) - (Σκ)2 n(Σαν)- (Σx)Σ) n (Σx2) - (Σκ)2 ή =

Sample size (n): 8

Mean x (x̄): 14.25

Mean y (ȳ): 34.5

Intercept (a): 9.594

Slope /Coeff of X (b): 1.748

Regression line equation is thus given by :

Y = 9.594 +1.748 X

(c) Correlation coefficien is given by

r = 0.948

Γ' = η Σε εigi - Σε : ΣΕ νη Σα– (ΣΕ, αι)?) (η Σ19 – (ΣΕ yi)2)

For linear regression : R ^ 2 = r*r = 0.898

(d) Y= 9.594 + 1.748*60

Y = 114.474

12. Z score is given by :

X= mean + std.dev * Z

Find the corresponding percentile for Z by looking in the body of the Z-table and finding the probability that is closest to p where p is the percentile you want to find.

(a) top 35% .

Take mean 0 and var 1

So Z = 0.385

Therefore , X = 0.385

(b) z= -0.84162

Then , X = (-0.84162 * 5.00000) + 75.00000

X= 70.791

(c) z = 0

X = 0