Let's examine the table and the temperature trend over different weeks:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Week} & \text{Average Temperature (°C)} \\
\hline
1 & 24.4 \\
\hline
2 & 24.8 \\
\hline
5 & 26.1 \\
\hline
8 & 27.2 \\
\hline
15 & 30.1 \\
\hline
24 & 33.6 \\
\hline
\end{array}
\][/tex]
When we plot these data points and perform a linear regression analysis, we can observe the following trend:
1. The slope of the trend line, [tex]\(0.40042643923240945\)[/tex], is positive.
2. This indicates that as the weeks increase, the temperature also increases.
As the slope is positive, we recognize an increasing trend.
The equation of the trend line based on the linear regression is [tex]\( y = 0.40042643923240945x + 24.029424307036233 \)[/tex], where:
- [tex]\( x \)[/tex] is the number of weeks,
- [tex]\( y \)[/tex] is the average temperature.
To predict the average temperature for the 26th week using the trend line equation:
[tex]\[
\begin{align*}
y & = 0.40042643923240945 \times 26 + 24.029424307036233 \\
& = 34.44051172707888 \ \text{°C}
\end{align*}
\][/tex]
Thus:
- The data shows an increasing trend.
- Based on the table, we can assume that the city's average weekly temperature in the 26th week will be 34.44051172707888°C.
