Question

1) The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 1313 varieties of Kellogg's cereal.

Sugar (grams)	5	15	12	11	8	6	7	3	8	14	20	4	13
Calories	130	200	160	110	120	80	190	120	120	190	190	130	120

Find the predictive regression equation of the number of calories on the amount of sugar.
Carry out all calculations exactly, and round the final answers to three decimal places.

(This is a multiple choice problem, please pick the correct answer out of the following.)

^y=97.932+4.658x

^y=97.932−4.658x

^y=4.658+97.932x

^y=−188.222+5.658x

^y=5.658+188.222x

2) The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 1313 varieties of Kellogg's cereal.

Sugar (grams)	6	15	12	11	8	6	7	4	9	14	20	3	13
Calories		120	160	110	140	80	210	100	120	190	190	130	120

The predictive regression equation of the number of calories on the amount of sugar is ^y=95.676+4.892xy^=95.676+4.892x, where xx is amount of sugar (in grams) and yy is calories.

Give a brief interpretation of the values of a=95.676 and b=4.892 in the equation. (this is also M/C, please pick the correct answer for a and b).

The value of a=95.676

means that, on average, the # of calories increases by one for every 95.676 gram increase in sugar?

means that, on average, the # of calories increases by 95.676 for every one gram increase in sugar?

represents the number of calories when the amount of sugar is zero?

The value of b=4.892

means that, on average, the # of calories increases by one for every 4.892 gram increase in sugar?

represents the number of calories when the amount of sugar is zero?

means that, on average, the number of calories increases by 4.892 for every one gram increase in sugar?

Answer 1

1.

Y.My (X-M.)2 22.0178 X - My -4.6923 5.3877 2.3077 1.3077 -1.6923 -3.6923 -2.6923 -6.6923 -1.6923 4.3077 10.3077 -5.6923 3.3077 - 13.8769 56.9231 16.9231 -33.8769 -23.8769 -63.8769 46.9231 -23.8769 -23.8769 46.9231 46.9231 - 13.8769 -23.8769 28.1716 5.3254 1.7101 2.8639 13.6331 7.2485 44.787 2.8639 18.5562 106. 2485 32.4024 18.9488 (X-MXY.My 61.36e9 302.1302 39.8533 -43.2544 39.0533 232.8994 - 126.3314 154.4379 39.0533 202.1302 483.6686 74.4379 -76.3314 SS: 296.7692 SP: 1382.3077

Sum of X = 126
Sum of Y = 1860
Mean X = 9.6923
Mean Y = 143.0769
Sum of squares (SS_X) = 296.7692
Sum of products (SP) = 1382.3077

Regression Equation = ŷ = bX + a

b = SP/SS_X = 1382.31/296.77 = 4.658

a = M_Y - bM_X = 143.08 - (4.66*9.69) = 97.932

ŷ = 4.658X + 97.932

So correct answer here is ^y=97.932+4.658x