Question

The time required for a sum of money to double in value, when compounded annually, depends upon the annual interest rate, as shown in the table. Use this data to find the equation of its trendline.

  

Annual Interest Rate (in %)	Time (in years)
4	17.7
5	14.2
6	11.9
7	10.2
8	9.0
9	8.0
10	7.3

		y = -2.5772x + 19.4239
		y = -1.6607x + 22.8110
		y = -1.0001x + 45.2846
		y = -0.5698x + 32.9841

2.

A manufacturing firm produces electronic circuits for a tool company. The firm claims to produce an average of 200 electronic circuits per hour for an 8-hour work day. Analyze and interpret the given data. Is this claim correct? Why or why not?

  

Hour #1	250 electronic circuits
Hour #2	190 electronic circuits
Hour #3	210 electronic circuits
Hour #4	195 electronic circuits
Hour #5	180 electronic circuits
Hour #6	200 electronic circuits
Hour #7	200 electronic circuits
Hour #8	70 electronic circuits

		This claim is correct. The firm produces a mean of 200 hammers per hour.
		This claim is correct. The firm produces a mode of 200 hammers per hour.
		This claim is correct. The firm produces a median of 200 hammers per hour.
		This claim is incorrect. The average does not equal 200 hammers per hour.

Answer 1

• Here let X be the independent random variable denoting the interest rate and let Y be the dependent random variable denoting time .
• Now we will calculate the sum of squares of x and y
• =371.00-(7*7.00²)=28.00
• =958.9-(7*11.2²)=83.0
• =501.6-(7*7.00*11.2)=-46.5

• Hence the coefficient of variable is given by

• The slope is given by b=Sxx/syy=-46.5/28=-1.660

• The intercept is given by

• 

• =11.2-(-1.660*7)

• =22.810

• Hence the regression line is given by

• y = -1.6607x + 22.8110

• which is option 2)