ght? According lave you ever oticed crickets chirping on a warm summer to resear

Question

ght? According lave you ever oticed crickets chirping on a warm summer to research, the amount crickets chirp can possibly be used to predict outdoor temperature The llowing analysis represents the relationship between cricket chirps per second and outdoor temperature oF for andom sample of 21 summer evenings. Cricket chirps per second vs Temperature Residuals 15 16 17 18 19 20 15 16 17 18 19 20 Chips per Second Chirps per Second Estimate std. Error t value Pr Iti (Intercept) 35.7855 10. 3462 3.459 0.002630 2.6388 0.5997 4.400 0.000308 Chirps Use the R output to answer the following questions. You can use the equation editor or to show your

Explanation / Answer

1. Linearity: The residual doesn't deviate from 0 in a systematic way ( i.e. residuals are positive for small x-values, negative for medium x-values and positive again for large x-values or the other way-round). Since there is no systematic pattern in the residual plot, linearity assumption is satisfied.

2. Normality: Since the residuals are uniformly distributed above and below the x-axis and the number of points above and number of points below x-axis are almost same and also plot is random, so the normality assumption holds true.

3. Constant variability: Constant variance or homoscedasticity assumption can be violated in a residual in two ways: (i) the residuals are close to 0 for small x-values (predictor values) and spread out for large x-values or, (ii) the residuals are large for small x-values and small for large x-values. But it is not the case here, since the residuals are uniformly distributed. So the constant variance assumption has been met.

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