1. Derive the linear relationship between Fahrenheit and Celsius? Since the rela

Question

1. Derive the linear relationship between Fahrenheit and Celsius? Since the relationship is linear, you only need two points to calculate the relationship, like the following Fahrenheit Celsius Freezing point of water 32 Boiling point of water 212 100 Use the slope-intercept form for the equation of a straight-line mx b, where m is the slope coefficient and b is the vertical intercept to derive the relationship. The equation for the slope is Ay/Ax, where Ay -yi yo and Ax X1 xo. Let y be the Fahrenheit temperature, and x be the Celsius temperature Note: To calculate the vertical intercept, use the fact that the vertical intercept is the value of y when x 0. Use a t-test to test the following hypotheses: The estimated slope coefficient is equal to the slope coefficient calculated in 1 above. The estimated constant is equal to the vertical intercept calculated in 1 above

Explanation / Answer

Question 1

Here, we have to use the slope-intercept form for the regression line or equation.

Slope = y / x

y = y1 – y0 = 212 – 32 = 180

x = x1 – x0 = 100 – 0 = 100

Slope = m = y / x = 180/100 = 1.8

When x =0, y = 32

So, y-intercept = 32

Regression equation given as below:

Y = mx + b

Where, m is slope and b is y-intercept

Y = 1.8*X + 32

Or

Y = 32 + 1.8*X

Question 2

For the estimated slope coefficient m = 1.79 or 1.8, the p-value is given as 0.00 approximately which is very less. So, we reject the null hypothesis that the estimated slope coefficient is not statistically significant. This means we conclude that the given slope is statistically significant.

For the estimated constant or Y-intercept = 32.69 or 32, the p-value is given as 0.00 approximately which is very less than the level of significance or alpha value of 0.05. so, we reject the null hypothesis that the intercept or constant for the given regression line is not statistically significant. This means we conclude that the given constant is statistically significant.

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