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Question 21 of 41
Q.

The information about death rate of a state in different years is given in the following table. Fit a linear equation to find trend and hence estimate the death rate for the year 2023.

Year2015201620172018201920202021
Death rate7.66.97.17.37.26.96.9
Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 5mImportance★★★★★
51% · 21/41 Questions
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Origin 2018, t=−3..3t=-3..3, Σt2=28\Sigma t^2=28; a=7.1286a=7.1286, b=−2.0/28=−0.0714b=-2.0/28=-0.0714; y^=7.13−0.071t\hat{y}=7.13-0.071t; 2023 (t=5t=5): y^≈6.77\hat{y}\approx\mathbf{6.77}.

Data (n=7n=7): Years 2015–2021; death rate yy: 7.6, 6.9, 7.1, 7.3, 7.2, 6.9, 6.9.

Coding: take the middle year 2018 as origin (t=0t=0), unit = 1 year.

Yearyyttt2t^2tyty
20157.6-39-22.8
20166.9-24-13.8
20177.1-11-7.1
20187.3000
20197.2117.2
20206.92413.8
20216.93920.7
Σ49.9028-2.0

Step 1 — constants (since Σt=0\Sigma t=0). …

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