Question

Annual high temperatures in a certain location have been tracked for several years. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, calculate the linear regression equation using technology (each constant to 2 decimal places).

x	y
2	34.82
3	33.28
4	34.84
5	35.1
6	33.26
7	35.42
8	34.18
9	34.54
10	34.4
11	35.86
12	35.12
13	37.88

The equation is?

Interpret the slope

• For each additional 0.2 years, the annual high temperature will increase by 1 degree on average.
• For each additional year, the annual high temperature will increase by 33.41 degrees on average.
• For each additional year, the annual high temperature will increase by 0.2 degrees on average.
• For each additional 33.41 years, the annual high temperature will increase by 1 degree on average.

Interpret the y-intercept

• It does not make sense to interpret the intercept in this scenario.
• In 2002, the temperature was about 0.2.
• In 2013, the temperature was about 37.88.
• In 2000, the temperature was about 33.41.
• In 2002, the temperature was about 33.41.

Answer 1

Sol:

Performed regression in minitab

STAT>Regression>Regression>Fit regression model

select response as Y

Indoendent variable as X clcik ok

STAT>REGRESSION>Fittted line plot

Regression Analysis: y versus x

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 5.573 5.573 5.16 0.047
x 1 5.573 5.573 5.16 0.047
Error 10 10.809 1.081
Total 11 16.382

Model Summary

S R-sq R-sq(adj) R-sq(pred)
1.03966 34.02% 27.42% 0.00%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 33.411 0.718 46.55 0.000
x 0.1974 0.0869 2.27 0.047 1.00

Equation is

y = 33.41 + 0.20x
slope=0.2,for unit increase in x,y increases by 0.2 on an average

For each additional year, the annual high temperature will increase by 0.2 degrees on average.

It does not make sense to interpret the intercept in this scenario.