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The human visual system excels at extracting ensemble statistics, facilitating the interpretation of complex visual information (Alvarez, 2011; Whitney, Haberman, & Sweeny, 2014; Utochkin, Choi, & Chong, 2024). However, this remarkable capability is not immune to bias. Our findings reveal that even seemingly unambiguous visual properties—such as estimating correlations from scatterplots, a task people generally perform with reasonable accuracy (Rensink, 2022)—can be influenced by belief-driven biases (Wolfe & Utochkin, 2019). We conducted an eye-tracking experiment where participants viewed scatterplots depicting meaningful variable pairs (e.g., number of environmental regulations and air quality) and estimated their correlations. They also viewed the same scatterplots with generic axes (‘X’ and ‘Y’). We analyzed the correlation derived from participants’ eye fixation points and discovered that it approximated the true correlation, slightly overshooting in the generic baseline condition (MD =0.149, SD = 0.329). For both plausible and implausible variable pairs, gaze-derived correlations also approximated the true correlation but consistently fell below those in the baseline condition, with the implausible condition showing a larger deviation. More interestingly, the dynamic analysis revealed a time-dependent impact of plausibility on gaze-derived correlations. The gaze-derived correlations significantly differed between conditions only in the first two seconds, and they plateaued near the true correlation values across all conditions within five seconds. This suggests that the plausibility of the scatterplot influences eye-gaze patterns most prominently during the initial viewing stages, suggesting that early engagement is critical for detecting belief-driven differences in perception. These results illustrate that prior beliefs can influence the perception of unambiguous visual properties like scatterplot correlation. This phenomenon, a form of belief-driven "motivated perception" (Geisler & Kersten, 2002), underscores the challenges scientists face when presenting data to persuade—our perceptions are often biased by our beliefs, even when viewing objective data points.