Question

pls answer ASAP. THANKS

Q1. Here are the data from a small bookstore:

Number of Salespeople
Working
Sales (in $1000s)
2 10
3 11
7 13
9 14
10 18
10 20
12 20
15 22
16 22
20 26
a. Compute the correlation coefficient between number of salespeople and sales.
Interpret the correlation coefficient.

b. Assuming the conditions for regression are met, find the estimated least-squares
regression line and predicted sales on a day with 12 employees working.

c. If you expect the population regression coefficient to be positive, perform the
hypothesis test of the regression coefficient at significance level of 0.05.

d. Find 95% prediction interval for Sales on a day with 12 employees working.

e. Comment on the overall quality of the fitted model using appropriate index

Answer 1

Solution

Given that:-

a)

total sum	104.00	176.00	286.40	256.40	261.60
mean	10.40	17.60	SSxx	SSyy	SSxy

correlation coefficient ,

there is positive , strong and linear correlation between two variables

so, we increase the number of sales person, sales will increase

................

b)

Sample size, n = 10
here,



  
estimated slope ,
intercept
  
Regression line is,

Predicted Y at X= 12 is

..

c)

slope hypothesis test


n= 10
alpha = 0.05
estimated std error of slope
t stat = estimated slope/std error

Degree of freedom ,df = n-2= 8
  
p-value = 0.0000
decison : p-value< , reject
Conclusion: Reject and conclude that slope is significantly different from zero

............

d)

standard error,
margin of error,
Prediction Interval Lower Limit
Prediction Interval Upper Limit
PI ( 15.4747 , 22.6482)

.............

E)

Approximately 93.19% of variation in observations of variable Y, is explained by variable x