The manager of a chain of furniture stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief he records last month's sales and the years of experience for 30 randomly selected salespeople. The linear regression output to predict Monthly Sales (in $1,000's) based on Years of Experience is:

SUMMARY OUTPUT

Regression Statistics

Multiple R. 0.6921

R Square 0.479

Observations 30

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 18.5 4.608 4.017 0.0004 9.1 27.9

Years of Experience 1.82 0.3587 5.074 0.0000 1.09 2.55

(a)Construct a 90% confidence interval for the population slope. [3 marks]

ANSWER:

(b)One of your salespeople with 12 years of experience had $25,000 in sales last month. Is this low for a salesperson with 12 years of experience?Explain using the regression line. [2]

(c)Interpret r² (the coefficient of determination) using the words of the problem.[2 marks]

(d)Is there enough evidence to conclude there is a linear relationship between monthly sales and years of experience?Test at the 5% significance level (95% confidence level).

H₀ H_A [2]

Apply a Rule + Decision

[2]

Conclusion:Circle the Correct One[1 mark]

A.Yes, there is enough evidence to conclude there is a linear relationship

B.No, there is not enough evidence to conclude there is a linear relationship