Following table shows the number of traffic fatalities (in a state) resulting from drunken driving from years 1975 to 1983:Years197519761977197819791980198119821983No. of deaths0638294510Fit a trend line by least square method.

Q.6 (A) (iii) Following table shows the number of traffic fatalities (in a state) resulting from drunken driving from years 1975 to 1983:

Years	1975	1976	1977	1978	1979	1980	1981	1982	1983
No. of deaths	0	6	3	8	2	9	4	5	10

Fit a trend line by least square method.

Doubtly Asked 28 Oct 2026 Board exam · June 2026 hsc 12th Save WhatsApp Report

1 answer

Best answer

Answer: \(y=5.222+0.667u\), where \(u=t-1979\)

\(n=9\) (odd), so take \(u=t-1979\).

Year \(t\)	\(y\)	\(u=t-1979\)	\(u^2\)	\(uy\)
1975	0	−4	16	0
1976	6	−3	9	−18
1977	3	−2	4	−6
1978	8	−1	1	−8
1979	2	0	0	0
1980	9	1	1	9
1981	4	2	4	8
1982	5	3	9	15
1983	10	4	16	40
Total	47	0	60	40

Trend line \(y=a+bu\) with \(a=\frac{\sum y}{n}=\frac{47}{9}=5.222\) and \(b=\frac{\sum uy}{\sum u^2}=\frac{40}{60}=0.667\).

\(\therefore\) The trend line is \(y=5.222+0.667u\), \(u=t-1979\). (Trend values: 1975: 2.555, 1979: 5.222, 1983: 7.889.)

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?